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$Given the definitions of f(x) and g(x) below, find the value of (g@f)(0). {:[f(x)=-x-4],[g(x)=x^(2)-4x-15]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $(g \circ f)(0)$ . $\newline$ $\begin{array}{l} f(x)=-x-4 \\ g(x)=x^{2}-4 x-15 \end{array}$ $\newline$ 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

(g \circ f)(0)

.

\newline

\begin{array}{l} f(x)=-x-4 \\ g(x)=x^{2}-4 x-15 \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 $f(x)$ . $\newline$ $f(x) = -x - 4$ $\newline$ $f(0) = -(0) - 4$ $\newline$ $f(0) = -4$
Calculate $g(f(0))$ : Now, we need to find the value of $g(f(0))$ by substituting $f(0)$ into $g(x)$ . $\newline$ $g(x) = x^2 - 4x - 15$ $\newline$ $g(f(0)) = g(-4) = (-4)^2 - 4*(-4) - 15$
Evaluate $g(-4)$ : Next, we calculate the value of $g(-4)$ .
$g(-4) = 16 - (-16) - 15$
$g(-4) = 16 + 16 - 15$
$g(-4) = 32 - 15$
$g(-4) = 17$

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