A function f : X → Y invertible if and only if f is

Question

A function \(f : X \rightarrow Y\) invertible if and only if f is

(A) one-one 

(B) onto 

(C) one-one and onto 

(D) None of these

Answer 1

Correct option is (C) one-one and onto

A function \(f: X \to Y\) is defined to be invertible, if there exist a function \(g = Y \to X\) such that \(gof = I_X\) and \(fog = I_Y\). The function is called the inverse of \(f\) and is denoted by \(f^{-1}\).

A function \(f=X \to Y\) is invertible if \(f\) bijective functions.

Answer 2

Correct option is (C) one-one and onto