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$Given the definitions of f(x) and g(x) below, find the value of f(g(0)). {:[f(x)=-5x-6],[g(x)=x^(2)-3x-10]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $f(g(0))$ . $\newline$ $\begin{array}{l} f(x)=-5 x-6 \\ g(x)=x^{2}-3 x-10 \end{array}$ $\newline$ Answer:

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Evaluate an exponential function

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

f(g(0))

.

\newline

\begin{array}{l} f(x)=-5 x-6 \\ g(x)=x^{2}-3 x-10 \end{array}

\newline

Answer:

Find $g(0)$ : First, we need to find the value of $g(0)$ by substituting $x$ with $0$ in the function $g(x)$ .
$g(x) = x^2 - 3x - 10$
$g(0) = (0)^2 - 3(0) - 10$
$g(0) = 0 - 0 - 10$
$g(0) = -10$
Substitute $g(0)$ into $f(x)$ : Now that we have $g(0) = -10$ , we substitute $-10$ into the function $f(x)$ to find $f(g(0))$ .
$f(x) = -5x - 6$
$f(g(0)) = f(-10)$
$f(-10) = -5(-10) - 6$
$f(-10) = 50 - 6$
$f(x)$ $0$

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