Question

What are the removable and non-removable discontinuities, if any, of `f(x)=(x^4 - 1)/(x-1)`?

Answer 1

Removable discontinuity at `x =1`

Explanation:

In a fractional function, discontinuities are caused by the denominator. We know that the denominator CANNOT be equal to 0.

Hence, `x - 1` cannot be equal to 0
In other words, x cannot be equal to 1, which is the value of x at which the function presents a discontinuity.

Since, there's only 1 value of x for which the function is not defined, it is a removable discontinuity.