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$g(x)=-20-3x$ $\newline$ $h(x)=(\frac{1}{2})^x$ $\newline$ Evaluate. $\newline$ $(g \circ h)(-2) =$

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Evaluate an exponential function

Full solution

Q.

g(x)=-20-3x

\newline

h(x)=(\frac{1}{2})^x

\newline

Evaluate.

\newline

(g \circ h)(-2) =

Understand $(g@h)(-2)$ : First, we need to understand what $(g@h)(-2)$ means. The notation $(g@h)(x)$ means that we first apply the function $h$ to $x$ , and then apply the function $g$ to the result of $h(x)$ . So, we need to find $h(-2)$ first.
Find $h(-2)$ : Now, let's find $h(-2)$ using the function rule $h(x) = (\frac{1}{2})^x$ . $\newline$ $h(-2) = (\frac{1}{2})^{-2}$
Calculate $h(-2)$ : Calculate $h(-2)$ . $h(-2) = (\frac{1}{2})^{-2}$ $= 2^2$ $= 4$
Find $g(4)$ : Now that we have $h(-2) = 4$ , we need to find $g(4)$ using the function rule $g(x) = -20 - 3x$ . $\newline$ $g(4) = -20 - 3(4)$
Calculate $g(4)$ : Calculate $g(4)$ . $g(4) = -20 - 3(4)$ $= -20 - 12$ $= -32$
Final Result: Therefore, $(g@h)(-2)$ is equal to $g(h(-2))$ , which we have found to be $g(4) = -32$ .

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