Answer
a.
$f^{-1}(x) = \sqrt[3] x/\sqrt[3]3$
b.
$f(f^{-1}(x)) = 3(\sqrt[3] x/\sqrt[3]3)^{3} $
$f(f^{-1}(x)) = 3x/3$
$f(f^{-1}(x)) = x$
$f^{-1}(f(x)) = \sqrt[3] 3x^{3}/\sqrt[3]3$
$f^{-1}(f(x)) = \sqrt[3]x^{3}$
$f^{-1}(f(x)) = x$
Work Step by Step
a.
$f(x) = 3x^{3}$
$x = 3f^{-1}(x)^{3}$
$x/3 = f^{-1}(x)^{3}$
$\sqrt[3] x/\sqrt[3]3 = f^{-1}(x)$
b.
$f(f^{-1}(x)) = 3(\sqrt[3] x/\sqrt[3]3)^{3} $
$f(f^{-1}(x)) = 3x/3$
$f(f^{-1}(x)) = x$
$f^{-1}(f(x)) = \sqrt[3] 3x^{3}/\sqrt[3]3$
$f^{-1}(f(x)) = \sqrt[3]x^{3}$
$f^{-1}(f(x)) = x$
