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

  1. #1
    rcs
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    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

    please help me on this
    thank you
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  2. #2
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    Quote Originally Posted by rcs View Post
    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}.
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  3. #3
    rcs
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    thanks plato...

    i still cant get the your hint. am i bit confused.
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  4. #4
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    Quote Originally Posted by rcs View Post
    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.
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