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$Given the definitions of f(x) and g(x) below, find the value of g(f(0)). {:[f(x)=2x+2],[g(x)=x^(2)+7x-11]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $g(f(0))$ . $\newline$ $\begin{array}{l} f(x)=2 x+2 \\ g(x)=x^{2}+7 x-11 \end{array}$ $\newline$ 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

g(f(0))

.

\newline

\begin{array}{l} f(x)=2 x+2 \\ g(x)=x^{2}+7 x-11 \end{array}

\newline

Answer:

Find $f(0)$ : First, we need to find the value of $f(0)$ by substituting $x$ with $0$ in the function $f(x)$ .
$f(0) = 2(0) + 2$
$f(0) = 0 + 2$
$f(0) = 2$
Calculate $g(f(0))$ : Now that we have $f(0) = 2$ , we need to find the value of $g(f(0))$ which is $g(2)$ . We substitute $x$ with $2$ in the function $g(x)$ . $\newline$ $g(2) = (2)^2 + 7(2) - 11$ $\newline$ $g(2) = 4 + 14 - 11$ $\newline$ $g(2) = 18 - 11$ $\newline$ $f(0) = 2$ $0$

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