Invertible function $f(x) = \frac{x^3}{3} + \frac{5x}{3} + 2 $ How can I prove that $f(x) = \frac{x^3}{3} + \frac{5x}{3} + 2 $ is invertible. 
First I choose variable $x$ for $y$ and tried to switch and simplified the function but I am  stuck. Need some help please.

Both $g(x)=\frac{x^3}3$ and $h(x)=\frac{5x}3+2$ are increasing functions. (This should be clear if you know graphs of some basic functions.)
Sum of two (strictly) increasing functions is again an increasing function, therefore $f(x)=g(x)+h(x)$ is strictly increasing.
If a function is strictly increasing, then it is injective.
