Question

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

Answer 1

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\\eq y(\because 2\\eq-2)`

This completes our proof by contradiction.