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$Given the definitions of f(x) and g(x) below, find the value of g(f(-8)). {:[f(x)=x+13],[g(x)=x^(2)+5x-11]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $g(f(-8))$ . $\newline$ $\begin{array}{l} f(x)=x+13 \\ g(x)=x^{2}+5 x-11 \end{array}$ $\newline$ Answer:

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Transformations of quadratic functions

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

g(f(-8))

.

\newline

\begin{array}{l} f(x)=x+13 \\ g(x)=x^{2}+5 x-11 \end{array}

\newline

Answer:

Find $f(-8)$ : First, we need to find the value of $f(-8)$ by substituting $-8$ into the function $f(x)$ . $\newline$ Calculation: $f(-8) = (-8) + 13$
Calculate $f(-8)$ : Now, we calculate the value of $f(-8)$ . $\newline$ Calculation: $f(-8) = -8 + 13 = 5$
Find $g(f(-8))$ : Next, we need to find the value of $g(f(-8))$ by substituting $f(-8)$ into the function $g(x)$ . $\newline$ Calculation: g(f(\(-8)) = g( $5$ ) = ( $5$ )^ $2$ + $5$ ( $5$ ) - $11$
Calculate $g(5)$ : Now, we calculate the value of $g(5)$ . $\newline$ Calculation: $g(5) = 5^2 + 5(5) - 11 = 25 + 25 - 11$
Find $g(5)$ : Finally, we add and subtract the numbers to find the value of $g(5)$ . $\newline$ Calculation: $g(5) = 25 + 25 - 11 = 50 - 11 = 39$

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