Answer :
Answer:4,-1
Step-by-step explanation:
A function [tex]f(x)[/tex] is said to have vertical asymptote at a point [tex]x_{0}[/tex] if [tex]f(x_{0})[/tex] tends to infinity or negative infinity.
Given function is [tex]f(x)=\frac{1}{(x-4)(x+1)}[/tex]
When [tex]x=4[/tex],
[tex]f(x)=\frac{1}{(4-4)(4+1)}=\frac{1}{0}[/tex]
[tex]f(4)[/tex]→∞
So,[tex]f(x)[/tex] has a vertical asymptote at [tex]4[/tex].
When [tex]x=-1[/tex],
[tex]f(x)=\frac{1}{(4+1)(-1+1)}=\frac{1}{0}[/tex]
[tex]f(-1)[/tex]→∞
So,[tex]f(x)[/tex] has a vertical asymptote at [tex]-1[/tex].
So,[tex]4,-1[/tex] are the vertical asymptotes of [tex]f(x)[/tex]
At values 4 and -1, the function F(x) has a vertical asymptote
