Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 345: 85

See explanation

Although the function has a finite positive slope $almost$ everywhere (which normally means that it is strictly increasing and is hence one-one), it is discontinuous* as can be seen in the graph of y=tan(x). So, it is not one-to-one. For example, $f(\pi/3) = f(7\pi/3) =\sqrt 3 $ *It is discontinuous on all the odd multiples of $\pi/2$