# Proof of Continuity – A split function with exponential functions – Exercise 6230

Exercise

Given the function

$$f(x) = \begin{cases} \frac{e^x-e^{-x}}{2}, &\quad x> 0\\ 0, &\quad x= 0\\ \frac{e^x-e^{-x}}{e^x+e^{-x}}, &\quad x<0\\ \end{cases}$$

Is it continuous?