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

1 Answer
Jan 16, 2018

Removable discontinuity at #x =1#


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.