SOLUTION
Given the question in the image, the following are the solution steps to get the discontinuity of the function
Step 1: Write the given function

Step 2: Define discontinuity of a function
A function has a removable discontinuity at x=a if

f(x) has step discontinuity if one-sided limits exist and finite but not equal.
f(x) has infinite discontinuity if one or both of the one-sided limits don't exist or are infinite
Step 3: State the infinite discontinuity and the removable discontinuity
To get the removable discontinuity

To get the infinite discontinuity

Hence, the discontinuity is removable at x=1 and infinite at x=-5
Option D