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Let
g(x)=8x-5. Which of the following is equivalent to
g(g(x)) ?
Choose 1 answer:
(A)
64 x-10
(B)
64 x-45
(c)
64x^(2)+25
(D)
64x^(2)-80 x+25

Let $g(x)=8 x-5$ . Which of the following is equivalent to $g(g(x))$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $64 x-10$ $\newline$ (B) $64 x-45$ $\newline$ (C) $64 x^{2}+25$ $\newline$ (D) $64 x^{2}-80 x+25$

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Compare linear and exponential growth

Full solution

Q. Let

g(x)=8 x-5

. Which of the following is equivalent to

g(g(x))

?

\newline

Choose

1

answer:

\newline

(A)

64 x-10

\newline

(B)

64 x-45

\newline

(C)

64 x^{2}+25

\newline

(D)

64 x^{2}-80 x+25

Understanding composition of functions: Understand the composition of functions. $\newline$ To find $g(g(x))$ , we need to substitute the function $g(x)$ into itself. This means we will replace every $x$ in $g(x)$ with the expression $8x - 5$ .
Substituting $g(x)$ into itself: Substitute $g(x)$ into itself. $\newline$ $g(g(x)) = g(8x - 5)$ $\newline$ We know that $g(x) = 8x - 5$ , so we replace $x$ with $(8x - 5)$ in the expression for $g(x)$ . $\newline$ $g(8x - 5) = 8(8x - 5) - 5$
Simplifying the expression: Simplify the expression. $\newline$ Now we distribute the $8$ inside the parentheses: $\newline$ $8(8x - 5) - 5 = 64x - 40 - 5$ $\newline$ Combine like terms: $\newline$ $64x - 40 - 5 = 64x - 45$
Checking the answer choices: Check the answer choices. $\newline$ We have simplified $g(g(x))$ to $64x - 45$ . Now we compare this with the given answer choices. $\newline$ (A) $64x - 10$ $\newline$ (B) $64x - 45$ $\newline$ (C) $64x^2 + 25$ $\newline$ (D) $64x^2 - 80x + 25$ $\newline$ The correct answer is (B) $64x - 45$ .

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