Question

Let A = {–1, 1} and B = {0, 2}. If the function f: A → B defined by f(x) = ax + b is an onto function? Find a and b

Answer 1

A = {–1, 1}; B = {0, 2}

f(x) = ax + b

f(–1) = a(–1) + b

0 = –a + b

a – b = 0 ….(1)

f(1) = a(1) + b

2 = a + b

a + b = 2 ….(2)

Solving (1) and (2) we get

a – b = 0    ....(1)
a + b = 2   ....(2)

(1) + (2) ⇒ 2a = 2

a = `(2)/(2)` = 1

Substitute a = 1 in (1)

The value of a = 1 and b = 1