Consider the functions given by

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

Problem

Consider the functions

f,g:\mathbb{R}\to \mathbb{R}

given by

f(x)=2x+3, \quad g(x)=\dfrac{1}{x-5}

(x\neq5)

. (a) Find the expression for

(g\circ f)(x)

. (b) Determine the domain of

(g\circ f)

. (c) Find the expression for

(f\circ g)(x)

together with its domain.