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$Given the definitions of f(x) and g(x) below, find the value of f(g(-4)). {:[f(x)=-5x+9],[g(x)=2x^(2)+2x-13]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $f(g(-4))$ . $\newline$ $\begin{array}{l} f(x)=-5 x+9 \\ g(x)=2 x^{2}+2 x-13 \end{array}$ $\newline$ Answer:

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

f(g(-4))

.

\newline

\begin{array}{l} f(x)=-5 x+9 \\ g(x)=2 x^{2}+2 x-13 \end{array}

\newline

Answer:

Find $g(-4)$ : First, we need to find the value of $g(-4)$ by substituting $x = -4$ into the function $g(x)$ . $g(-4) = 2(-4)^2 + 2(-4) - 13$
Calculate $g(-4)$ : Now, let's calculate $g(-4)$ . $\newline$ $g(-4) = 2(16) - 8 - 13$ $\newline$ $g(-4) = 32 - 8 - 13$ $\newline$ $g(-4) = 24 - 13$ $\newline$ $g(-4) = 11$
Find $f(g(-4))$ : Next, we need to find the value of $f(g(-4))$ by substituting $g(-4)$ into the function $f(x)$ . $\newline$ $f(g(-4)) = f(11)$ $\newline$ $f(11) = -5(11) + 9$
Calculate $f(11)$ : Finally, let's calculate $f(11)$ . $\newline$ $f(11) = -55 + 9$ $\newline$ $f(11) = -46$

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