Determine (f∘g)(x) when f(x)=2x2+2x−2 and g(x)=−2x2+x−1.

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Lesson Parent: 
Function Composition
Problem: 

Determine (f∘g)(x) when f(x)=2x2+2x−2 and g(x)=−2x2+x−1.

Answer: 

(f∘g)(x)=f(g(x))=8x4−8x3+6x2−2x−2

SAMPLE SOLUTION

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Solution: 

Recall our lesson on function composition.

Our first step in determining <Sign in to see all the formulas> is to replace x by g in f(x). This gives <Sign in to see all the formulas>. Next place the formula g(x) into every value of g in f(g) to obtain

<Sign in to see all the formulas>