Let be defined by where

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

Problem

Let

f:\mathbb R \to \mathbb R

be defined by

f(x)=kx+1

where

k\in\mathbb R

, and let

g:[0,\infty)\to\mathbb R

be defined by

g(t)=\sqrt t

. For which value(s) of

k

is the composition

g\circ f

defined for every real

x

? (a)

k\ge 0

(b)

k\le 0

(c)

k=0

(d) No real

k

satisfies the requirement