Respuesta :
Answer:
Removable discontinuity at [tex]x=4[/tex].
Step-by-step explanation:
We have been given a function [tex]g(x) = \frac{x^2-9x+20}{x-4}[/tex]. 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.
[tex]g(x)=\frac{x^2-5x-4x+20}{x-4}[/tex]
[tex]g(x)=\frac{x(x-5)-4(x-5)}{x-4}[/tex]
[tex]g(x)=\frac{(x-5)(x-4)}{x-4}[/tex]
Cancelling out (x-4):
[tex]g(x)=x-5,x\neq 4[/tex]
This means that at [tex]x=4[/tex] our given function is not defined and it has removable point discontinuity at [tex]x=4[/tex].
