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


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?

Final Answer

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


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