Chapter 6 - Review Exercises - Page 499: 11

$f^{-1}(x)=x^2+2$

$f(x)=\sqrt{x-2},$ $y=\sqrt{x-2},$ $x=\sqrt{y-2},$ $x^2=\sqrt{y-2},$ $y=x^2+2=f^{-1}(x),$ Checking the inverse function.. $(f\circ f^{-1})(x)=\sqrt{x^2+2-2}=\sqrt{x^2}=x$ $(f^{-1}\circ f)(x)=(\sqrt{x-2})^2+2=x-2+2=x$