Question

Prove or disprove the statement, If f(x) = f(y), then x=y

Answer 1

Answer:

The given statement can be disproved by giving a simple counter-example

Using proof by contradiction method:

Let

$f(x)=x^{2}$

Let

$x=2\\\\\therefore f(2)=2^{2}=4$

Let

$y=-2\\\\\therefore f(-2)=(-2)^{2}=4$

As we can see that

$f(x)=4\\\\f(y)=4\\\\\therefore f(x)=f(y)\\\\But\\x\neq y(\because 2\neq-2)$

This completes our proof by contradiction.