Question

Prove that f:Z--Z defined by f(x) = 1 + x^2 is not one-one.​

Answer 1

Step-by-step explanation:

f(x) = x² + 1

let x = -1

=> f(-1) = (-1)² + 1

=> f(-1) = 2

let x = 1

=> f(1) = 1² + 1

=> f(1) = 2

now f(-1) = f(1) which implies element in codomain has two pre images OR two different elements in the domain are related to one element in the co domain hence the given relation is not one - one