# Proof of Continuity – A split function with rational functions and parameters – Exercise 6594

Exercise

Given the function

$$f(x) = \begin{cases} {(\frac{1-x}{1+x})}^{\frac{c}{x}}, &\quad x>0\\ e^2, &\quad x = 0\\ {(a+bx)}^{\frac{1}{x}}, &\quad x<0\\ \end{cases}$$

a,b and c are parameters. For which values of the parameters the function is continuous?

$$a=1, b=2, c=-1$$