Answer
True
Work Step by Step
Let $n=2a+1$ where a is an integer. This notation will remind us that n is an odd number.
So, $f(x)=x^n = x^{2a+1}$
Therefore, $f'(x) = (2a+1)x^{2a}$ is always of the same sign because $x^{2a}$ is always positive. Furthermore, we know that $x^n $ is a polynomial and polynomials are continuous everywhere. Thus $f(x) $ is one-to-one and hence invertible.
Alternatively, we could have assumed $x_1$ and $x_2$ such that $f(x_1)=f(x_2)$ and then prove that it implies $x_1=x_2$
