Mathematics

Problem

Define

h:\mathbb R\to(0,\infty)

h(x)=e^{x^{3}}

. Which statement is correct? a)

h

is bijective and

h^{-1}(y)=\ln y^{1/3}

. b)

h

is injective only and

h^{-1}(y)=\sqrt[3]{\ln y}

. c)

h

is bijective and

h^{-1}(y)=\sqrt[3]{\ln y}

. d)

h

is bijective and

h^{-1}(y)=\dfrac{1}{3}\ln y