Consider the linear function defined by where

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

Problem

Consider the linear function

f:\mathbb R\to\mathbb R

defined by

f(x)=mx+c

where

m\neq0

. Suppose a function

g:\mathbb R\to\mathbb R

of the form

g(x)=px+q

is its inverse. (i) Write the expressions for

(f\circ g)(x)

and

(g\circ f)(x)

. (ii) By equating each composition to the appropriate identity function, determine

p

and

q

in terms of

m

and

c