Answer:
Option A
Step-by-step explanation:
The complete question is shown in the attachment.
Note that: [tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
We need to multiply all the functions to see which of them satisfy the given criteria.
Option A
[tex]x^2\cdot \frac{1}{x} =\frac{x^2}{x}=x[/tex]
Option B
[tex]\frac{2}{x} \cdot \frac{2}{c} =\frac{4}{cx}[/tex]
Option C
[tex]\frac{x-2}{3} \cdot 2-3x =\frac{-3x^2+8x-4}{3}[/tex]
Option D
[tex]\frac{1}{2x-2} \cdot \frac{1}{2x+2} =\frac{1}{4(x^2-1)}[/tex]
The correct choice is A
