# Proof of Continuity – A split function with A quotient of functions with a square root and a parameter – Exercise 6250

Exercise

Given the function

$$f(x) = \begin{cases} \frac{\sqrt{x^2+11}-6}{x^2-25}, &\quad 5\neq x>0\\ c, &\quad x=5 \\ \end{cases}$$

c parameter. For what value of c is the function continuous at point x = 5?

$$c=\frac{1}{12}$$