Determine $(f\circ g)(x)$ when $f(x)=-x^2-8\,x-6$ and $g(x)=9\,x^2+4\,x+3$.

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Lesson Parent: 
Function Composition
Problem: 

Determine $(f\circ g)(x)$ when $f(x)=-x^2-8\,x-6$ and $g(x)=9\,x^2+4\,x+3$.

Answer: 

$(f\circ g)(x)=f(g(x))=-81\,x^4-72\,x^3-142\,x^2-56\,x-39$

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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

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