Question

What are the removable and non-removable discontinuities, if any, of `f(x)=(2x^2+5x-12 )/( x+4)`?

Answer 1

There is a removable discontinuity at x=-4.
There is no, non-removable discontinuity.

Explanation:

In the above expression due to (x+4) in the denominator, f(x) becomes undefined at x=-4, Hence there is a discontinuity at x=-4. However this (x+4) gets cancelled by (x+4) in the numerator, which makes f(x) = 2x-3. which is continuous.

This discontinuity at x= -4 is called the removable discontinuity.