Browse Questions

# True or False: Every function is invertible.

Toolbox:
• A function f is invertible if it is one-one and onto
A function $f:N \to N$

$f(x)=x^2$

Let $x_1\; and\; x_2$ be such that $x_1,x_2 \in N$

$f(x_1)=f(x_2)$

$=>x_1=x_2$

But we see that for $y=2 \in N$

There does not exist $f(x)=2$

Therefore f is not onto

f is not invertible

Hence the given statement is 'False'