Engineering Board Exam Reviewer · Functions: Domain, Composition, and Inverses · medium

If f(x+1)=x2+3x, find f(x).

1. f(x)=x2+3x
2. f(x)=x2+5x+4
3. f(x)=x2-x-2
4. f(x)=x2+x-2

Answer

D. f(x)=x2+x-2

Solution

Let u=x+1, so x=u-1: f(u)=(u-1)2+3(u-1)=u2-2u+1+3u-3=u2+u-2. Hence f(x)=x2+x-2.

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