Question

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

As $f\left(1\right)=f(-1)$, so the function $f\left(x\right)$ can't be one-one.