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Math Help - Difference Quotient

  1. #1
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    Difference Quotient

    Find the difference quotient of f, that is, find [f(x + h) - f(x)]/h, where h cannot = 0, for the given function.

    Be sure to simplify.

    f(x) = 1/(x + 3)

    NOTE: This question comes from a precalculus textbook and so the explanation must be in precalculus terms and NOT calculus.
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  2. #2
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    Hello,

    Quote Originally Posted by magentarita View Post
    Find the difference quotient of f, that is, find [f(x + h) - f(x)]/h, where h cannot = 0, for the given function.

    Be sure to simplify.

    f(x) = 1/(x + 3)

    NOTE: This question comes from a precalculus textbook and so the explanation must be in precalculus terms and NOT calculus.
    Hmmm well, this doesn't involve calculus, only algebra

    f(x+h)=\frac{1}{(x+h)+3}

    So \frac{f(x+h)-f(x)}{h}=\frac{\frac{1}{x+h+3}-\frac{1}{x+3}}{h}

    Now, get the common denominator of the numerator and put it on the same fraction.

    Remember : \frac ab+\frac cd=\frac{ad}{bd}+\frac{cb}{bd}=\frac{ad+bc}{bd}

    Can you finish ?
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  3. #3
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    Yes..I can

    Yes, I can finish now.

    I got stuck in terms of the value of x in the fraction 1/(x + 3).

    I did not see that x = (x + h).

    Thanks
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