Let be defined by and by

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

f:\mathbb R\to\mathbb R

be defined by

f(x)=ax+b

and

g:\mathbb R\to\mathbb R

g(x)=cx+d

, where

a,c\neq 0

. For

f

and

g

to be mutual inverses, which one of the following sets of conditions on the constants must hold? (a)

ac=1,\; ad-b=0,\; cb+d=0

(b)

ac=1,\; ad+b=0,\; cb-d=0

(c)

ac=1,\; ad+b=0,\; cb+d=0

(d)

ac=-1,\; ad+b=0,\; cb+d=0