For a real parameter

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

k

, consider the function

f_{k}:\mathbb R\to\mathbb R

defined by

f_{k}(x)=kx^{3}+x

. (a) Determine all real values of

k

for which

f_{k}

is injective. (b) For the values of

k

found in part (a), state whether

f_{k}

is surjective and hence invertible.