Define by . Which statement is…

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define

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

by

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

.

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