Solution:
The given function is
f(x)= [tex]\frac{4 x^2- 4 x -8}{2 x}[/tex]
f(x)= [tex]\frac{4 x^2}{2 x}-\frac{4 x}{2x} -\frac{8}{2x}\\\\ = 2 x -2 -\frac{4}{ x}[/tex]
f(x)= 2 x - 2 - [tex]\frac{4}{x}[/tex]
To find the points of Discontinuity
Put, f(x)=0
→ 2 x - 2 - [tex]\frac{4}{x}[/tex]=0
→2 x² - 2 x - 4=0×x
→2 (x²-x-2)=0
→ x² - x -2=0
Splitting the middle term
→ x² - 2 x + x -2=0
→ x×(x-2)+ 1 × (x-2)=0
→ (x+1) (x-2)=0
Gives, x= -1, and x=2.
So, the graph represented by f(x)= [tex]\frac{4 x^2- 4 x -8}{2 x}[/tex] is equal to f(x)= 2 x - 2 - [tex]\frac{4}{x}[/tex] with points of Discontinuity at -1 and 2.
