For the parameter

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

For the parameter

a\in\mathbb{R}

, define

f_a(x)=\sqrt{x+a}

and

g(t)=\dfrac{1}{t-2}

. (i) Determine all real values of

a

for which

(g\circ f_a)(x)

is defined for at least one real

x

. (ii) For

a=3

, find the domain of

(g\circ f_a)(x)