How do you solve composite functions examples?

Answers

Answer 1

The composite function is the result of first applying the function (x^2 - 1) to the input and then applying the function (5x + 2) to the result. The final result of the composite function is 5x^3 + 2x - 3.

Step 1: Apply (x^2 - 1) to the input:

(x^2 - 1) = x^2 - 1

Step 2: Apply (5x + 2) to the result:

(5x + 2)(x^2 - 1)

= 5x^3 - 5x + 2x - 2

Step 3: Simplify:

5x^3 - 5x + 2x - 2

= 5x^3 + 2x - 3

A composite function is the result of applying two or more functions in succession. The order of operations for a composite function is to first apply the first function, then apply the second function to the result of the first, and so on. In the example given, the composite function

f(x) = (5x + 2) ∘ (x^2 - 1)

is the result of first applying the function

(x^2 - 1)

to the input and then applying the function (5x + 2) to the result. The calculation can be broken down into three steps: Step 1 is to apply (x^2 - 1) to the input to get x^2 - 1, Step 2 is to apply (5x + 2) to the result to get 5x^3 - 5x + 2x - 2,

and Step 3 is to simplify the result to get the final answer of

5x^3 + 2x - 3.

To summarize, the composite function

f(x) = (5x + 2) ∘ (x^2 - 1)

is the result of first applying the function (x^2 - 1) to the input, and then applying the function (5x + 2) to the

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Related Questions

Jenna noted the prices for a bag of dog food at a number of online stores. The prices were $22, $9, $10, $19, $18, and $20.

Find the mean, median, and mode of the prices.
Which measure of center BEST describes this set of data. Explain your choice.

Answers

Answer:

Mean: 16.333333333333

Median: 18.5

Mode: 9,10,18,19,20,22

Step-by-step explanation:

Mean: Add all the terms together and divide your result by the amount of you there are. ((22+9+10+19+18+20) / 6)

Median- Organize the terms from least to greatest. When you find the middle of the terms you will get 18.5, look for what between 18 and 19.

Mode- Normally to find the mode you would order the terms from least to greatest, and then find which term occurs the most. But since all the terms occur once, it will be all of the terms.

6 is what percent of 88?

Answers

Answer:

6 is 6.82% of 88

If a mom has 3 kids who are 18, 16, and 26 how old is the mother
and how old was she when she gave birth

30 POINTS BEST ANSWER WILL GET BRAINLIEST

Answers

Answer:

Step-by-step explanation:

If the firstborn arrived 26 years ago, his mother's age was likely between 20 and 30 years old when she gave birth.  Her current age is likely between 46 and 56 years.

What is the surface area of the cylinder with height 7 in and radius 6 in? Round your answer to the nearest thousandth.

Answers

Surface area is 490.088

Answer: 490.088 in2

Step-by-step explanation:

Pula need to make an 80% on her test to pass the class. she has 25 questions on the test. How many does she need to get correct

Answers

Answer:

Step-by-step explanation:

25×80%=20

so she need to get 20 questions right

Answer:

20

Step-by-step explanation:

total question: 25

marks need to pass: 80%

25-20% = 20

help please i really need help​

Answers

Answer:$ 1341.99

Step-by-step explanation: Hope its helps

The students at Walden Middle School are selling tins of popcorn to raise money for new uniforms. They sold 42 tins in the first week.How much money did they make in the first week?

Answers

Answer:

$388.50

Step-by-step explanation:

42 tins

$9.25/tin

[tex]42*9.25=388.5[/tex]

So, they raised $388.50

what is the quotient of 6x^3+2x-x/x where x≠0

Answers

Answer:

6[tex]x^{2}[/tex] + 1

Step-by-step explanation:

[tex]\frac{6x^{3}+ 2x-x }{x}[/tex]   combine 2x -x = x

[tex]\frac{6x^{3} + x}{x}[/tex]

[tex]\frac{x(6x^{2} + 1) }{x}[/tex]  the x's cancel out

6[tex]x^{2}[/tex] + 1

The three angles of a triangle have measures of 65 degrees, 15 degrees, and (x +42) degrees. What is x?

please !!! only a couple minutes left!! help

Answers

Answer:

58 degree is the value of x

20 PTS-what Theorem can be used to prove these triangles are congruent

Answers

Answer: AAS

Step-by-step explanation:

AAS, because the side congruence isn't between the angles as it should be in order for it to be ASA.

please help just answer the blanks I'll give a crown thing don't waste an answer.​

Answers

Answer:

5) 1: 63

  2: 117

  3: 63

  4: 117

  5: 63

  6: 117

  7: 63

  8: 117

Step-by-step explanation:

Vertical, corresponding, alternate exterior, and alternate interior angles are all congruent (equal).Angles such as same side exterior and same-side interior are supplementary; meaning these angles add up to 180°.

Sammies room is 20 feet long and 12 feet wide her parents want to cover the floor with tiles. If they choose to use tiles with with side 2 feet long how many tile would they need

Answers

Find the area of the room by multiplying the length by the width:

Area of room = 20 x 12 = 240 square feet.

Find the area of the tile: 2x 2 = 4 square feet.

To find the number of tiles divide the area of the room by the area of a tile:

240/4 = 60

They will need 60 tiles.

Answer:

120

Step-by-step explanation:

20*12=240

240/2=120

A math club is having a bake sale. Find the area of the bake sale sign.


The Area of the sign is_ square feet

Answers

The bake sale sign has a 6 ft2 space.

What is area?

An object's area is how much space it takes up in two dimensions.

It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space.

A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.

But a shape's area is a two-dimensional measurement. In order to measure something in a square, it is done so using measurements like square inches (in2), square feet (ft 2), square yards (yd2), etc.

The majority of forms and things have corners and edges. 

According to our question-

The opposite sides of a rectangle's quadrilateral (it has four sides and four angles) are equal and parallel.

Area of a rectangle equals length times width.

The area of the bake sale sign = length * breadth

Hence, The bake sale sign has a 6 ft2 space.

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The lengths of the four sides of a quadrilateral (in centimeters) are consecutive even integers. If the perimeter is 132 centimeters, find the value of the shortest of the four side lengths.

Answers

The value of the shortest of the four side lengths of the quadrilateral is 30 cm

What is the length of the shortest side of the quadrilateral?

The perimeter of a quadrilateral is the sum of all the sides.

Perimeter of the Quadrilateral = 132 centimeters

Let

The shortest side = x

Since, the sides are consecutive even integers;

Second side = (x + 2)

Third side = (x + 4)

Fourth side = (x + 6)

Perimeter of the Quadrilateral = shortest side + Second side + Third side + Fourth side

132 = x + (x + 2) + (x + 4) + (x + 6)

132 = x + x + 2 + x + 4 + x + 6

132 = 4x + 12

132 - 12 = 4x

120 = 4x

divide both sides by 4

x = 120/4

x = 30 centimeters

Therefore,

Second side = (x + 2)

= 30 + 2

= 32 cm

Third side = (x + 4)

= 30 + 4

= 34 cm

Fourth side = (x + 6)

= 30 + 6

=36 cm

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15. A pool can hold 850 gallons. It now has 598 gallons of
water and is being filled at the rate shown. How many
more minutes, m, can water continue to flow into the
pool before it overflows? Write and solve an inequality.
Then graph the solutions.

Answers

850 >= 598+15.75m
252 >= 15.75m
16>=m
The pool can be filled for 16 minutes before it overflows

Which polynomial is prime?
x3 + 3x2 -2x - 6
x° - 2x2 + 3x 6
4x4 + 4x3 - 2x - 2
D 2x + x3 -x +2

Answers

The final equation is a polynomial of primes  [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored. Variables are sometimes known as indeterminate in mathematics.

what is polynomial ?

 An essential component of the "language" of mathematics and algebra are polynomials. They are used to express numbers that are the result of mathematical operations in almost every area of mathematics. Other types of mathematical expressions, such as rational expressions, also use polynomials as "building blocks."

given

Is a base form of a polynomial in other words is a polynomial that can't be factored.

so we have

[tex]A ) x^{3} +3x^{2} - 2x - 6 = ( x +3 ) ( x^{2} - 2 )\\B) x^{3} -2x^{2} +3x - 6 = ( x- 2 ) (x^{2} + 3)\\C)4x^{4} +4x^{3} - 2x - 2 = 2( x +1 )(2x^{2} - 1)\\D) 2x^{4} +x^{3} -x + 2[/tex]

hence, the final equation is a polynomial of primes  [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored.

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I need help please thx God bless you

Answers

Answer:

A. 3/4 or .75

B.  5/6 or .83333

C. 11/12 or .91667

D. 1/20 or .05

Step-by-step explanation:

A. 1/2 + 1/4 = 3/4 or .75

B. 1/2 + 1/3 = 5/6 or .83333

a. 1/4 + 2/3 = 11/12 or .91667

b. 1/4 - 1/6 = 1/20 or .05

Do the ratios 5/15 and 1/3 form a proportion?

Answers

Answer:

Step-by-step explanation:

We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.

5/15 = 1/3

5*3 = 15*1

15 = 15

as the left-hand side is equal to the right side. So, these fractions are in proportion.

Write two equivlants ratios for each ratios
a. 3:12
b) 3/5
c) 108:9
help meeeeeee plsssss begging u

Answers

Step-by-step explanation:

[tex]3 : 12 \equiv \frac{3}{12} \equiv 1 : 4[/tex]

[tex] \frac{3}{5} \equiv3 : 5[/tex]

[tex]108 : 9 \equiv \frac{108}{9} \equiv12 : 1[/tex]

A cuboid has a volume of 24 cm^3. What can its maximum surface area be, if its length, breadth, and height are integers?

Answers

Answer:

76 cm^2

Step-by-step explanation:

Volume of the cuboid = Length(l)×breadth(b)×Height (h)

Given that

A cuboid has a volume of 24 cm^3 and its length, breadth, and height are integers only.

prime factor of 24 = [tex]2^3\times3\times1[/tex]

24 = 2×3×2×2×1

24= 12×2×1

or 24= 6×4×1

Now, for Surface area to be maximum we have to take dimensions as

12,2,1

SA = 2(lb+lh+bh)

=2(12×2+12×1+2×1)

= 76 cm^2

Therefore, maximum area of the cuboid with diemensions, 12,2,1 = 76 unit

Hi, please help (see image)
I need help on question b) and c)
This homework is due very soon !!! ( SOS)

Answers

Answer:

b: Two thousand four hundred and forty (2440)

c: 1.33 x 10^27

Step-by-step explanation:

I'm uncertain by what an ordinary number is, but to calculate the answer for part b, you need to divide the diameter of Mercury by 2, which would give the aforementioned answer.

As for part c, you will need to subtract the masses of Jupiter and Saturn:
mass of Jupiter - mass of Saturn = 1.33 ×[tex]10^{27}[/tex]

What is the length of the hypotenuse of a 45 45 90 triangle if the length of the leg is 5?

Answers

The length of the hypotenuse will be 5√2 = 7.07

The triangle specified in the question is right-angled, one angle is mentioned to be 90°. It is also an isosceles triangle since both other angles are equal. if both angles are equal, both sides will also be equal.

So the length of both equal sides = 5 cm

Pythagoras' theorem tells us about the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse of the right-angled triangle will be equal to the sum of squares of the other two sides. If a, b, and c are the sides

 c² = a²+ b²

  c = √(a²+b²)

According to Pythagoras' theorem, Hypotenuse = √base²+ alt²

                                                          Hypotenuse = √5²+5²

                                                                                = 5√2

                                                                               = 7.07 cm

So the length of the hypotenuse is 5√2 = 7.07 cm.

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Help plis and thankyou :)

Answers

hola cómo estás yo muy bien y tu qué tal

HELP

Find the Axis of Symmetry

Answers

Answer:

Axis of symmetry= 3

Step-by-step explanation:

f(x)= 2x^2 +12x-4

f(x)=ax^2+bx+c

x=12/2(2)

x=3

f(x)= 2(3)^2+12(3)-14

f(x)= 2(9)+36-14

f(x)=18+36-14

f(x)= 54-14

y=40

by using the distributive property and the greatest common factor what is 18+15

Answers

Answer:

33

Step-by-step explanation:

18 + 15 ← factor out 3 ( the GCF ) from each term

= 3(6 + 5)

= 3(11)

= 3 × 11

= 33

Solve correctly for brainly

Answers

Answer:

y=4x+26

Step-by-step explanation:

x intercept =( [tex]\frac{- 13}{2} \\[/tex], 0)

y intercept = (0,26)

1) Convert point-slope equation to slope-intercept:

y - 6 = 4x + 20
y = 4x + 26

2) Find the x-intercept:

0(y) = 4x + 26
0 = 4x + 26
-26 = 4x
x = (-13/2 , 0)

3) Find the y-intercept:

y = 4(0) + 26
y = 0 + 26
y = (0 , 26)

PLEASE HELP NOW IM BEGGING AND PLEADING PLEASE AND THANK YOU
Linear sequences & graphs 206 - Straight line graphs 1 Quiz 1 2 3 4 5 6 7 8 6 of 8 Use the table to work out the values of a , b , c , and d . x y = 5 − 3 x − 3 a − 2 11 − 1 b 0 5 1 c 2 d a = b = c = d =

Answers

The values of a, b, c and d are -5, -1, 3 and 5.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=2x+1

Substitute (-3, a) in y=2x+1, we get

a=2(-3)+1

a=-6+1

a=-5

Substitute (-1, b) in y=2x+1, we get

b=2(-1)+1

b=-1

Substitute (1, c) in y=2x+1, we get

c=2(1)+1

c=3

Substitute (2, d) in y=2x+1, we get

d=2(2)+1

d=5

Therefore, the values of a, b, c and d are -5, -1, 3 and 5.

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"Your question is incomplete, probably the complete question/missing part is:"

Use the table to work out the values a, b, c and d.

      x        y=2x+1

     -3           a

     -2           -3

      -1           b

       0            1

       1            c

       2            d

The waitress had a table with a bill of $75.29 and received $12.80. What was the percent tip she received?

Answers

None they didn’t give the right amount

Answer:

17%

Step-by-step explanation:

Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%

Willl mark you brainlieestttt

Answers

A rational number is any integer, fraction, terminating decimal, or repeating decimal. So the irrational numbers are options B and C.

Answer:

√28 and √11

Step-by-step explanation:

Note : -

Irrational number is any real number that cannot be expressed as the quotient of two integers.

Here,

√28 = 5.291.......

5.291.... is an infinite number, it keeps going, it cannot be expressed in terms of a fraction.

Similarly,

√11 = 3.316......

Hence,

√28 and √11 are irrational numbers.

Hays is standing outside on a sunny day. he is 6 ft tall and casts a 4 ft shadow. what is the distance from the top of hays's head to the end of his shadow? round to the nearest tenth, if necessary. responses
a. 4.5 ft
b. 4.5 ft
c. 5 ft
d. 5 ft
e. 7.2 ft
f. 7.2 ft
g. 10 ft

Answers

Options e and f is the correct answers. The distance from the top of hays' head to the end of his shadow is 7.21ft

Hays' body and his shadow are perpendicular.

So if we imagine the line from the top of his head to the end of his shadow on the ground, we have a right triangle, and the imaginary line is the hypotenuse.  

Then you can stand back and let Pythagoras figure out the length of the line for you, using c²  =  a² + b²

(Distance)²=(Hay's height)²+(length of his shadow)²

(Distance)²=(6 ft)² + (4 ft)²

(Distance)²=(36 ft²) + (16 ft²)

(Distance)=52 ft²

Distance =√(52 ft)²

Distance = 7.21 ft

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