Question

Is (fg)(0)=(f/g)(0)? Explain

Answer 1

Answer:

No, not in general, but you could say sometimes. See examples.

Step-by-step explanation:

Example 1: Choose $f(x)=e^x$ and $g(x)=x$

$(fg)(0)$

$(f(0))(g(0))$

$(e^0)(0)$

$(1)(0)$

$0$

$\frac{f}{g}(0)$

$\frac{f(0)}{g(0)}$

$\frac{e^0}{0}$

$\frac{1}{0}$ which is a not a number.

Example 2: Choose $f(x)=x-1$ and $g(x)=x-2$

$(fg)(0)$

$(f(0))(g(0))$

$(0-1)(0-2)$

$(-1)(-2)$

$2$

$\frac{f}{g}(0)$

$\frac{f(0)}{g(0)}$

$\frac{0-1}{0-2}$

$\frac{-1}{-2}$

$\frac{1}{2}$.

Example 3: Choose $f(x)=x$ and $g(x)=1$.

$(fg)(0)$

$(f(0))(g(0))$

$(0)(1)$

$0$

$\frac{f}{g}(0)$

$\frac{f(0)}{g(0)}$

$\frac{0}{1}$

$0$

So as you can see they are sometimes equal and sometimes not. It will depend on the functions.

Answer 2

I mean anything x0 is 0 so I believe the answer is 0