Let f(x) = 4x2–6 and g(x)=x–2. (a) Find the composite function (f∘g)(x) and simplify. Show work. (b) Find (f∘g)(−1). Show work.
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(a) The composite function is, (f∘g)(x)=f(g(x)) =f(x−2) =4(x−2)2−6 [replacing x by x−2∈f(x)] =4(x2−4x+4)−6 =4x2−16x+16−6 4x2−16x+10 b) Replacing x by -1 in the composite function, we get (f∘g)(−1)=4(−1)2−16(−1)+10 =4+16+10 =30
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