Respuesta :
Answer:
No, not in general, but you could say sometimes. See examples.
Step-by-step explanation:
Example 1: Choose [tex]f(x)=e^x[/tex] and [tex]g(x)=x[/tex]
[tex](fg)(0)[/tex]
[tex](f(0))(g(0))[/tex]
[tex](e^0)(0)[/tex]
[tex](1)(0)[/tex]
[tex]0[/tex]
[tex]\frac{f}{g}(0)[/tex]
[tex]\frac{f(0)}{g(0)}[/tex]
[tex]\frac{e^0}{0}[/tex]
[tex]\frac{1}{0}[/tex] which is a not a number.
Example 2: Choose [tex]f(x)=x-1[/tex] and [tex]g(x)=x-2[/tex]
[tex](fg)(0)[/tex]
[tex](f(0))(g(0))[/tex]
[tex](0-1)(0-2)[/tex]
[tex](-1)(-2)[/tex]
[tex]2[/tex]
[tex]\frac{f}{g}(0)[/tex]
[tex]\frac{f(0)}{g(0)}[/tex]
[tex]\frac{0-1}{0-2}[/tex]
[tex]\frac{-1}{-2}[/tex]
[tex]\frac{1}{2}[/tex].
Example 3: Choose [tex]f(x)=x[/tex] and [tex]g(x)=1[/tex].
[tex](fg)(0)[/tex]
[tex](f(0))(g(0))[/tex]
[tex](0)(1)[/tex]
[tex]0[/tex]
[tex]\frac{f}{g}(0)[/tex]
[tex]\frac{f(0)}{g(0)}[/tex]
[tex]\frac{0}{1}[/tex]
[tex]0[/tex]
So as you can see they are sometimes equal and sometimes not. It will depend on the functions.
