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$Given the definitions of f(x) and g(x) below, find the value of g(f(-3)). {:[f(x)=x^(2)+5x+13],[g(x)=-5x+4]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $g(f(-3))$ . $\newline$ $\begin{array}{l} f(x)=x^{2}+5 x+13 \\ g(x)=-5 x+4 \end{array}$ $\newline$ 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(-3))

.

\newline

\begin{array}{l} f(x)=x^{2}+5 x+13 \\ g(x)=-5 x+4 \end{array}

\newline

Answer:

Find $f(-3)$ : First, we need to find the value of $f(-3)$ by substituting $x$ with $-3$ in the function $f(x) = x^2 + 5x + 13$ . $\newline$ Calculation: $f(-3) = (-3)^2 + 5(-3) + 13$ $\newline$ $f(-3) = 9 - 15 + 13$ $\newline$ $f(-3) = -6 + 13$ $\newline$ $f(-3) = 7$
Calculate $g(f(-3))$ : Now that we have the value of $f(-3)$ , we can find $g(f(-3))$ by substituting the value of $f(-3)$ into the function $g(x) = -5x + 4$ .
Calculation: $g(f(-3)) = g(7) = -5(7) + 4$
$g(7) = -35 + 4$
$g(7) = -31$

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