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# Checking injectivity (TIFR 2013 problem 36)

Question:

True/False?

The function $$f:\mathbb{Z} \to \mathbb{R}$$ defined by $$f(n)=n^3-3n$$ is injective.

Hint:

Check for small values!

Discussion:

Surely, checking for small values will give you that f is not injective.

For example, let us look at $$f(0)=0$$, $$f(1)=-2$$, $$f(-1)=2$$, $$f(2)=2$$.

So $$f(-1) = f(2)$$.

Therefore, $$f$$ is not injective.

September 16, 2017