Let’s solve a problem based on checking injectivity from TIFR 2013 problem 36. Try it yourself first, then read the solution here.

**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.

## Some useful links:

*Related*

Google