Let and , where and . Assume and . If for all , what can you say about and…

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

Problem

Let

f(x)=ax+b

and

g(x)=cx+d

, where

a\neq0

and

c\neq0

. Assume

a=1

and

b=2

. If

(f\circ g)(x)=(g\circ f)(x)

for all

x

, what can you say about

c

and

d

? (a)

c

and

d

are both arbitrary. (b)

c=1

d

arbitrary. (c)

c

arbitrary,

d=1

. (d)

c=1

d=1