we are given
[tex]f(x)=\frac{x^2-5x}{x^2-x-20}[/tex]
Firstly, we will simplify it
[tex]f(x)=\frac{x(x-5)}{(x-5)(x+4)}[/tex]
[tex]f(x)=\frac{x}{(x+4)}[/tex]
At x=5.5:
we can plug x=5.5
[tex]f(5.5)=\frac{5.5}{(5.5+4)}[/tex]
[tex]f(5.5)=0.578947[/tex]
At x=5.1:
we can plug x=5.1
[tex]f(5.1)=\frac{5.1}{(5.1+4)}[/tex]
[tex]f(5.1)=0.56043956[/tex]
At x=5.05:
we can plug x=5.05
[tex]f(5.05)=\frac{5.05}{(5.05+4)}[/tex]
[tex]f(5.05)=0.558011[/tex]
At x=5.01:
we can plug x=5.01
[tex]f(5.01)=\frac{5.01}{(5.01+4)}[/tex]
[tex]f(5.01)=0.5560488[/tex]
At x=5.005:
we can plug x=5.005
[tex]f(5.005)=\frac{5.005}{(5.005+4)}[/tex]
[tex]f(5.005)=0.5558023[/tex]
At x=5.001:
we can plug x=5.001
[tex]f(5.001)=\frac{5.001}{(5.001+4)}[/tex]
[tex]f(5.001)=0.5556049[/tex]
At x=4.9:
we can plug x=4.9
[tex]f(4.9)=\frac{4.9}{(4.9+4)}[/tex]
[tex]f(4.9)=0.5505617[/tex]
At x=4.95:
we can plug x=4.95
[tex]f(4.95)=\frac{4.95}{(4.95+4)}[/tex]
[tex]f(4.95)=0.5530726[/tex]
At x=4.99:
we can plug x=4.99
[tex]f(4.99)=\frac{4.99}{(4.99+4)}[/tex]
[tex]f(4.99)=0.55506117[/tex]
At x=4.995:
we can plug x=4.995
[tex]f(4.995)=\frac{4.995}{(4.995+4)}[/tex]
[tex]f(4.995)=0.55503085[/tex]
At x=4.999:
we can plug x=4.999
[tex]f(4.999)=\frac{4.999}{(4.999+4)}[/tex]
[tex]f(4.999)=0.55550616[/tex]
