Let and be fixed real numbers with

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

Problem

Let

c

and

d

be fixed real numbers with

cd\neq 0

. Define

f: \mathbb R\setminus\left\{-\dfrac d c\right\}\to\mathbb R

f(x)=\frac{ax+b}{cx+d},

where

a,b

are real parameters and

ad-bc\neq 0

. Which of the following conditions on

a

and

d

ensures that

f(f(x))=x

holds for every permissible

x

? (a)

ad=1

(b)

a+d=0

(c)

d=a

(d)

b=-d