Question

If the function f : {-1, 1} → {0, 2} defined by f(x) = ax + b is a surjection, then find a and b.

Answer 1

Answer:

a = 1, b =1

Step-by-step explanation:

Concept:

A function f from set A to set B is called surjective if range of f is equal to co-donain(B)

Given: f(x) = ax +b

Since f is surjective,

Range = co-domain = { 0, 2}

f(-1) = 0 , - a + b = 0.....(1)

f(1) = 2, a + b = 2.....(2)

(1)+(2) 2b = 2

b = 1

put b=1 in (2) we get a = 1

I hope this answer helps you