# Proof of Continuity – A split function with a quotient of functions and parameters – Exercise 5867

Exercise

Given the function

$$f(x) = \begin{cases} \frac{x^2-8x-9}{3-\sqrt{x}}, &\quad x>9\\ ax+b-6, &\quad 0\leq x\leq 9\\ e^{\frac{1}{x}}, &\quad x<0\\ \end{cases}$$

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

$$a=-\frac{20}{3}, b=6$$