Question

Consider the following functions. f(x)=2x−7,g(x)=−x

2
(a) Find (f∘g)(x). (b) Find (g∘f)(x). (c) Find (f∘f)(x).

Answer 1

`\mathrm{Given:}\\f(x)=2x-7\\g(x)=-x\\\\\mathrm{a)\ \ }\\(fog)(x)=f(g(x))=2g(x)-7=2(-x)-7=-2x-7\\\\\mathrm{b)\ \ }\\(gof)(x)=g(f(x))=-f(x)=-(2x-7)=-2x+7\\\\\mathrm{c)\ \ }\\(fof)(x)=f(f(x))=2f(x)-7=2(2x-7)-7=4x-14-7=4x-21`