Question

The function $f:R\to R$ be defined by $f\left(x\right)=(x^2+1{)}^{35}$. Prove that the function $f\left(x\right)$ is not one-one.

Answer 1

Given the function $f:R\to R$ be defined by $f\left(x\right)=(x^2+1{)}^{35}$.

Now we have $-1\ne 1$ but $f\left(1\right)=2^{35}=f(-1)$.

So the function $f\left(x\right)$ is not one-one.