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

• Feb 5th 2011, 03:46 AM
rcs
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
• Feb 5th 2011, 04:13 AM
Plato
Quote:

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: $\displaystyle \dfrac{g(x+h)-g(x)}{h}=\dfrac{xhf(x)f(h)+hf(h)}{h}.$
• Feb 6th 2011, 03:31 AM
rcs
thanks plato...

i still cant get the your hint. am i bit confused.
• Feb 6th 2011, 03:59 AM
Plato
Quote:

Originally Posted by rcs
i still cant get the your hint. am i bit confused.

From the given:
$\displaystyle g(x+h)=g(x)g(h)$
$\displaystyle g(x)=xf(x)+1$
$\displaystyle g(h)=hf(h)+1$.

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

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