Math Help - can anybody prove the g'(x) = g (x)? please

1. can anybody prove the g'(x) = g (x)? please

Let f and g be two functions whose domains are the set of all real numbers. Furthermore, suppose that

g(x) = x f(x) + 1

g (a+b) = g(a) g(b) for all a and b

lim f(x) = 1
x-> 0

thank you

2. Originally Posted by rcs
Let f and g be two functions whose domains are the set of all real numbers. Furthermore, suppose that
g(x) = x f(x) + 1
g (a+b) = g(a) g(b) for all a and b
lim f(x) = 1
x-> 0
See if by using the given you can get: $\dfrac{g(x+h)-g(x)}{h}=\dfrac{xhf(x)f(h)+hf(h)}{h}.$

3. thanks plato...

i still cant get the your hint. am i bit confused.

4. Originally Posted by rcs
i still cant get the your hint. am i bit confused.
From the given:
$g(x+h)=g(x)g(h)$
$g(x)=xf(x)+1$
$g(h)=hf(h)+1$.

Now put it together and let $h\to 0$

If you still don't see, the sit down with a live tutor.