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$Given the definitions of f(x) and g(x) below, find the value of f(g(-2)). {:[f(x)=2x-3],[g(x)=3x^(2)+7x+12]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $f(g(-2))$ . $\newline$ $\begin{array}{l} f(x)=2 x-3 \\ g(x)=3 x^{2}+7 x+12 \end{array}$ $\newline$ Answer:

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Evaluate an exponential function

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

f(g(-2))

.

\newline

\begin{array}{l} f(x)=2 x-3 \\ g(x)=3 x^{2}+7 x+12 \end{array}

\newline

Answer:

Find $g(-2)$ : First, we need to find the value of $g(-2)$ by substituting $x$ with $-2$ in the function $g(x) = 3x^2 + 7x + 12$ . $\newline$ Calculation: $g(-2) = 3(-2)^2 + 7(-2) + 12$ $\newline$ $g(-2) = 3(4) - 14 + 12$ $\newline$ $g(-2) = 12 - 14 + 12$ $\newline$ $g(-2) = 10$
Calculate $f(g(-2))$ : Now that we have the value of $g(-2)$ , we can find $f(g(-2))$ by substituting $g(-2)$ into the function $f(x) = 2x - 3$ .
Calculation: $f(g(-2)) = f(10) = 2(10) - 3$
$f(10) = 20 - 3$
$f(10) = 17$

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