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

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3 votes

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

This completes our proof by contradiction.

User John Doe Smith
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