# Proof of Continuity – A split function with exponential functions with a parameter – Exercise 6248

Exercise

Given the function

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

c parameter. For what value of c is the function continuous at point x = 0?

$$c=\ln 2$$