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g(x)=-20-3x h(x)=((1)/(2))^(x) Evaluate. (g@h)(-2)=

g(x)=−20−3x g(x)=-20-3 x \newlineh(x)=(12)x h(x)=\left(\frac{1}{2}\right)^{x} \newlineEvaluate.\newline(g∘h)(−2)= (g \circ h)(-2)=

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Q. g(x)=−20−3x g(x)=-20-3 x \newlineh(x)=(12)x h(x)=\left(\frac{1}{2}\right)^{x} \newlineEvaluate.\newline(g∘h)(−2)= (g \circ h)(-2)=
  1. Understand Function Composition: Understand the composition of functions. The composition of two functions (g∘h)(x)(g \circ h)(x) means we first apply hh to xx, and then apply gg to the result of h(x)h(x).
  2. Evaluate h(−2)h(-2): Evaluate h(−2)h(-2).
    h(x)=(12)xh(x) = (\frac{1}{2})^x
    h(−2)=(12)−2=22=4h(-2) = (\frac{1}{2})^{-2} = 2^2 = 4
  3. Evaluate g(h(−2))g(h(-2)): Evaluate g(h(−2))g(h(-2)).\newlineNow we need to apply gg to the result from Step 22, which is 44.\newlineg(x)=−20−3xg(x) = -20 - 3x\newlineg(4)=−20−3(4)=−20−12=−32g(4) = -20 - 3(4) = -20 - 12 = -32
  4. Combine Results: Combine the results to find (g@h)(−2)(g@h)(-2).(g@h)(−2)=g(h(−2))=g(4)=−32(g@h)(-2) = g(h(-2)) = g(4) = -32

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