Chapter 6 Rational Exponents and Radical Functions - 6.4 Use Inverse Functions - 6.4 Exercises - Quiz for Lessons 6.3-6.4 - Page 445: 12

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Given: $f(x)=6x^2+1, x\geq0\\g(x)=(\frac{x-1}{6})^{1/2}$ Obtain: $g(f(x))=g(6x^2+1)=(\frac{6x^2+1-1}{6})^{1/2}=(\frac{6x^2}{6})^{1/2}=(x^2)^{1/2}=\sqrt x^2=x$ $f(g(x))=f((\frac{x-1}{6})^{1/2})=6((\frac{x-1}{6})^{1/2})^2+1=6.\frac{x-1}{6}+1=x-1+1=x$ $g(f(x))=f(g(x))=x$