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.

The function passes the horizontal line test, so it has an inverse function. The fact that the slope is always positive as the user44197 mentioned, implies that it passes the horizontal line test.
