For a real parameter

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

Problem

k

, let

f_k(x)=x^{2}+k\quad(x\in\mathbb{R}),\qquad g(x)=\sqrt{x}\;(x\ge0).

(i) In terms of

k

, find the range of

f_k

. (ii) Determine all real values of

k

for which the composition

(g\circ f_k)(x)

is defined for at least one real

x

. (iii) For each such

k

, obtain the largest possible domain of

(g\circ f_k)

and give the explicit expression of the composition on this domain.