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

Primary tabs

Lesson Parent: 
Function Composition
Problem: 

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

Answer: 

$(f\circ g)(x)=f(g(x))=-x^4+2\,x^3-3\,x^2+2\,x$

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



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>