For , let be defined by ( f_k(x)= kx 1+|x| ). Which one of the following statements…

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

Problem

For

k \neq 0

, let

f_k:\mathbb{R}\to(-2,2)

be defined by

f_k(x)=\frac{kx}{1+|x|}

. Which one of the following statements correctly describes the set of all values of

k

for which

f_k

is onto its codomain

(-2,2)

? (a) all real

k

satisfying

k=2

(b) all real

k

satisfying

|k|\ge 2

k

satisfying

|k|<2

(d) all real

k

satisfying

|k|\le 2