Let and . A function is defined by , , and , where…

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

Problem

Let

A = \{1,2,3,4\}

and

B = \{w,x,y,z\}

. A function

f: A \to B

is defined by

f(1)=w

f(2)=x

f(3)=y

and

f(4)=p

, where

p \in B

. (i) Write the range of

f

in terms of

p

. (ii) Determine all possible values of

p

for which

f

is bijective. (iii) For each value of

p

found in part (ii), write down the inverse mapping

f^{-1}