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$Given the definitions of f(x) and g(x) below, find the value of g(f(2)). {:[f(x)=3x^(2)-6x-9],[g(x)=5x-8]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $g(f(2))$ . $\newline$ $\begin{array}{l} f(x)=3 x^{2}-6 x-9 \\ g(x)=5 x-8 \end{array}$ $\newline$ Answer:

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

g(f(2))

.

\newline

\begin{array}{l} f(x)=3 x^{2}-6 x-9 \\ g(x)=5 x-8 \end{array}

\newline

Answer:

Find $f(2)$ : First, we need to find the value of $f(2)$ by substituting $x$ with $2$ in the function $f(x)$ . $\newline$ $f(2) = 3(2)^2 - 6(2) - 9$
Calculate $f(2)$ : Now, let's perform the calculations for $f(2)$ .
$f(2) = 3(4) - 12 - 9$
$f(2) = 12 - 12 - 9$
$f(2) = 0 - 9$
$f(2) = -9$
Find $g(f(2))$ : Next, we need to find the value of $g(f(2))$ . Since we have found that $f(2) = -9$ , we will substitute $x$ with $-9$ in the function $g(x)$ . $\newline$ $g(f(2)) = g(-9)$ $\newline$ $g(-9) = 5(-9) - 8$
Calculate $g(f(2))$ : Now, let's perform the calculations for $g(-9)$ . $g(-9) = 5(-9) - 8$ $g(-9) = -45 - 8$ $g(-9) = -53$

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