Question

Determine the value(s) of x at which the function is discontinuous. Describe the discontinuity as removale or non-removable.

Answer 1

Answer with explanation: To find the values of x where the f(x) is discontinuous, we have to set the denominator equal to zero, doing this gives:

`\begin{gathered} f(x)=(x^2+10+9)/(x^2-81)\Rightarrow x^2-81=0 \\ x=\sqrt[]{81}=9 \\ x=9 \end{gathered}`

The f(x) is discontinuous at x = 9, following graph confirms it:

In conclusion, discontinuity is non-removable.​