Let be defined by and be defined by .

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

Problem

Let

f: \mathbb R \to \mathbb R

be defined by

f(x)=2x-3

and

g: \mathbb R \to \mathbb R

be defined by

g(x)=x^{2}+4

. (i) Find

(g\circ f)(x)

and simplify. (ii) Find

(f\circ g)(x)

and simplify. (iii) Evaluate

(g\circ f)(2)

and

(f\circ g)(2)