Determine $(f\circ g)(x)$ when $f(x)=-x^2-5$ and $g(x)=x+5$.

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Lesson Parent: 
Function Composition
Problem: 

Determine $(f\circ g)(x)$ when $f(x)=-x^2-5$ and $g(x)=x+5$.

Answer: 

$(f\circ g)(x)=f(g(x))=-x^2-10\,x-30$

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

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