Question

In Exercise,discuss the continuity of the function.
g(x) = x^2-9x+20/x-4

Answer 1

Removable discontinuity at
`x=4`.

Explanation:

We have been given a function
`g(x) = (x^2-9x+20)/(x-4)`. We are asked to discuss the continuity of the given function.

We can see our given function is a rational function. We know that a rational function is continuous for all values except those, where denominator is zero.

First of all, we will try to factor the numerator of our given function.

`g(x)=(x^2-5x-4x+20)/(x-4)`

`g(x)=(x(x-5)-4(x-5))/(x-4)`

`g(x)=((x-5)(x-4))/(x-4)`

Cancelling out (x-4):

`g(x)=x-5,x\\eq 4`

This means that at
`x=4` our given function is not defined and it has removable point discontinuity at
`x=4`.