Question

for f(x)=x^2 + 9 and g(x)=x^2 - 3, find the following functions. a. (f ∘ g)(x); b. (g ∘ f)(x); c. (f ∘ g)(4); d. (g ∘ f)(4) a. (f ∘ g)(x)=x^4 - 6x^2 + 18 (simplify your answer.) b. (g ∘ f)(x)=x^4 + 18x^2 + 78 (simplify your answer.) c. (f ∘ g)(4)=

Explanation:

Step1: Recall the result of (f o g)(x)

We know that \((f\circ g)(x)=x^{4}-6x^{2}+18\).

Step2: Substitute x = 4

Substitute \(x = 4\) into \((f\circ g)(x)\): \((f\circ g)(4)=4^{4}-6\times4^{2}+18\).

Step3: Calculate powers

First, calculate \(4^{4}=256\) and \(4^{2} = 16\). Then the expression becomes \(256-6\times16 + 18\).

Step4: Calculate multiplication

Calculate \(6\times16=96\). So the expression is \(256 - 96+18\).

Step5: Calculate subtraction and addition

\(256-96 = 160\), and \(160+18=178\).

Answer:

178