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Math Help - Function help

  1. #1
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    Function help

    Hi there,

    I have a function problem which I'm having trouble solving, and I can't wait until class for the answer.

    If f(x) = x^2
    and
    g(x) = f(x + h) - f(x) all on h
    find
    g(2)

    The answer is apparently 4 + h.

    How would I get this answer? I keep getting just h on its own.

    thanks
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  2. #2
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    Re: Function help

    Quote Originally Posted by Caddym89 View Post
    Hi there,

    I have a function problem which I'm having trouble solving, and I can't wait until class for the answer.

    If f(x) = x^2
    and
    g(x) = f(x + h) - f(x) all on h
    find
    g(2)

    The answer is apparently 4 + h.

    How would I get this answer? I keep getting just h on its own.

    thanks
    I'm confused. If g(x)=f(x+h)-f(x) for all h, wouldn't it mean g(x)=0 especially when h=0?

    EDIT: Assuming g(x)=f(x+h)-f(h), we have

    g(2)=f(2+h)-f(h)=(2+h)^2-h^2=4+4h+h^2-h^2=4+4h
    Last edited by Gusbob; April 4th 2013 at 07:16 PM.
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  3. #3
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    Re: Function help

    Sorry, when I say g(x) = f(x + h) - f(x) all on h, I mean f(x + h) - f(x) is the numerator and h the denominator
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  4. #4
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    Re: Function help

    Oops must have misread that.

    Assuming h\not=0

    g(2)=\frac{f(2+h)-f(2)}{h}=\frac{(2+h)^2-4}{h}=\frac{4+4h+h^2-4}{h}=\frac{\not{h}(4+h)}{\not{h}}
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  5. #5
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    Re: Function help

    Thanks a lot Gusbob. I have been looking at this for hours and can't believe it was so simple >_<
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