Question

What is the discontinuity of the function `f(x)=(3x^2+x-4)/(x-1)`?

Answer 1

There is a removable discontinuity at `x=1`, where the numerator and denominator are both `0`, since:

`(3x^2+x-4)/(x-1) = ((x-1)(3x+4))/(x-1) = 3x+4`

with exclusion `x != 1`

Explanation:

Since we have this factorisation, `lim_(x->1) f(x)` exists and is equal to `3(1)+4 = 7`.

So the discontinuity is removable by redefining `f(1) = 7`