Let be defined by .

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

Problem

Let

f:\{1,2,3\}\to\{a,b,c,d\}

be defined by

f(1)=a,\;f(2)=b,\;f(3)=c

. (i) Define an injective function and a surjective function. (ii) Determine whether the given function

f

is injective. Give a reason for your answer. (iii) Determine whether

f

is surjective. Give a reason for your answer. (iv) Is

f

invertible? Justify your conclusion based on your answers to parts (ii) and (iii).