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Let $f(x)=2x+3$ and $g(x)=x^{2}-4x$ . $\newline$ Which of the following is equivalent to $g(f(x))$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $4x^{2}+4x-3$ $\newline$ (B) $4x^{2}-8x-3$ $\newline$ (C) $4x^{2}+4x+21$ $\newline$ (D) $2x^{2}-8x+3$

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Add and subtract integers: word problems

Full solution

Q. Let

f(x)=2x+3

and

g(x)=x^{2}-4x

.

\newline

Which of the following is equivalent to

g(f(x))

?

\newline

Choose

1

answer:

\newline

(A)

4x^{2}+4x-3

\newline

(B)

4x^{2}-8x-3

\newline

(C)

4x^{2}+4x+21

\newline

(D)

2x^{2}-8x+3

Substitute $f(x)$ into $g(x)$ : We need to find $g(f(x))$ . To do this, we will substitute the expression for $f(x)$ into $g(x)$ . The function $f(x)$ is given by $2x+3$ , so we will replace every $x$ in $g(x)$ with $2x+3$ .
Expand $(2x+3)^2$ : The function $g(x)$ is given by $x^2 - 4x$ . Substituting $f(x)$ into $g(x)$ , we get $g(f(x)) = (2x+3)^2 - 4(2x+3)$ .
Distribute $-4$ : Now we need to expand $(2x+3)^2$ . This is done by squaring both terms and the cross term: $(2x+3)(2x+3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9$ .
Combine terms: Next, we distribute the $-4$ in $-4(2x+3)$ to get $-8x - 12$ .
Simplify expression: Now we combine the results from Step $3$ and Step $4$ to get the full expression for $g(f(x))$ : $4x^2 + 12x + 9 - 8x - 12$ .
Simplify expression: Now we combine the results from Step $3$ and Step $4$ to get the full expression for $g(f(x))$ : $4x^2 + 12x + 9 - 8x - 12$ . Simplify the expression by combining like terms: $4x^2 + 12x - 8x + 9 - 12 = 4x^2 + 4x - 3$ .

More problems from Add and subtract integers: word problems

Question

g

can be thought of as a scaled version of

f(x)=|x|

\newline

What is the equation for

g(x)

\newline

1

\newline

g(x)=-\frac{4}{3}|x|

\newline

g(x)=\frac{4}{3}|x|

\newline

g(x)=-\frac{3}{4}|x|

\newline

g(x)=\frac{3}{4}|x|

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Question

y=|x|

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\newline

What is the equation of the new graph?

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\newline

y=-\frac{5}{3}|x|

\newline

y=\frac{3}{5}|x|

\newline

y=-|x-5|+3

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Question

\$ 200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

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t

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\mathrm{t}

t

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\newline

40 h+80 t=400

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80 h+40 t=200

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5 h+2.5 t=200

\newline

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Posted 10 months ago

Question

We want to find the intersection points of the graphs given by the following system of equations:

\newline

\left\{\begin{array}{l} x-y=-4 \\ y=5(x+1)^{2}-3 \end{array}\right.

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One of the intersection points is

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Find the other intersection point. Your answer must be exact.

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Question

\mathbf{2 2}

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x

dollars. Which of the following represents the total amount of money Derrick and Colleen have, in dollars?

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1

\newline

x-22

\newline

x+22

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22 x

\newline

22 x+22

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Question

Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of

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meters. He wants to increase the radius to

40

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\newline

(Round to the nearest thousand cubic meters.)

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Question

Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are

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42

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Question

Ari thinks the perfect milkshake has

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3

spoonfuls of caramel. Freeze Zone makes batches of milkshakes with

10

scoops of ice cream and

7

spoonfuls of caramel.

\newline

What will Ari think about the amount of caramel in Freeze Zone's milkshakes?

\newline

1

\newline

(A) Freeze Zone's milkshakes have too much caramel.

\newline

(B) Freeze Zone's milkshakes have too little caramel.

\newline

(C) Freeze Zone's milkshakes are just right.

Posted 8 months ago

Question

Nayeli lights a

4 \mathrm{~m}^{2}

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\newline

Whose space is lit brighter?

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(A) Nayeli's area

\newline

(B) Citlali's area

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Question

Lashawn makes scrambled eggs with

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\newline

Whose scrambled eggs have a stronger salsa taste?

\newline

1

\newline

(A) Lashawn's eggs

\newline

(B) Gilberta's eggs

\newline

(C) The dishes of scrambled eggs have equal salsa tastes.

Posted 8 months ago

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