Question

For the function $f\left(x\right)=\{\begin{array}{cc}\frac{(x-1)(9-x^2)}{x-1},& x\ne 1\\ 9,& x=1\end{array}$ which of the following statements is TRUE

• A. $f\left(x\right)$ has missing point discontinuity
• B. $f\left(x\right)$ has isolated point discontinuity
• C. $f\left(x\right)$ has finite type discontinuity
• D. $f\left(x\right)$ has infinite type discontinuity

Answer 1

The correct option is B $f\left(x\right)$ has isolated point discontinuity

​​​​​​For $f\left(x\right)=\frac{(x-1)(9-x^2)}{x-1},x\ne 1$​ curve is
at $x=1,f\left(1\right)$ is defined.
Here clearly limit exists but not equal to$f\left(1\right)$
Hence $f\left(x\right)$ has Isolated point discontinuity at $x=1$.