Chapter 6 Rational Exponents and Radical Functions - 6.4 Use Inverse Functions - 6.4 Exercises - Quiz for Lessons 6.3-6.4 - Page 445: 11

See below.

We need to show that $f(g(x))=x=g(f(x))$ $f(g(x))=f(-\frac{2}{3}x+\frac{1}{6})=-1.5(-\frac{2}{3}x+\frac{1}{6})+0.25=x-0.25+0.25=x$ $g(f(x))=g(-1.5x+0.25)=-\frac{2}{3}(-1.5x+0.25)+\frac{1}{6}=x-\frac{1}{6}+\frac{1}{6}=x$ Thus we proved what we had to.