Question

Consider the set A = {1, 2, 3, 4, 5}, and B = {1, 4, 9, 16, 25} and a function ƒ : A → B defined by f(1) = 1, f(2) = 4, f(3) = 9, f(4) = 16 and f(5) = 25

(i) Show that f is one-to-one

(ii) Show that f is onto.

(iii) Does ƒ^-1 exists? Explain

Answer 1

(i) ƒ = {(1,1), (2,4), (3,9), (4,16), (5,25)}

Every element in A is mapped to different elements in B. Therefore one-to-one.

(ii) R (ƒ) = {1, 4, 9, 16, 25} = B. Therefore onto.

(iii) Since f is one-to-one and onto function, ƒ^-1 exists.

ƒ^-1 = {(1,1), (4,2), (9,3), (16,4), (25,5)}