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Math Help - pre-calculus/functions help

  1. #1
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    pre-calculus/functions help

    hello all,

    question:

    f(x)=1/x   evaluate  f(x)-f(a)/x-a


    thank you
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  2. #2
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    f(x)-f(a)/x-a = 1/x-(1/a)*(1/x)-a = f(x)(1-1/a)-a

    or you can write it as

    f(x)-f(a)/x-a = 1/x-(1/a)*(1/x)-a = (a-1)/(a*x)-a
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  3. #3
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    Quote Originally Posted by str33tl0rd View Post
    hello all,

    question:

    f(x)=1/x evaluate  f(x)-f(a)/x-a


    thank you
    There is nowhere to start. It looks like you've got the slope of a secant line through a hyperbola (assuming that you meant to include parentheses).

    Do you have any more instruction?
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  4. #4
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    thank you for the help guy, but it seems like that wasn't the answer =|

    i think i have miswritten the question, i'll retry:

    if f(x)=1/x
    evaluate
    [f(x)-f(a)]/(x-a)

    and the answer is supposed to be: -1/ax

    i need a working out, thank you very much all you guys and girls
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  5. #5
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    Quote Originally Posted by str33tl0rd View Post
    thank you for the help guy, but it seems like that wasn't the answer =|

    i think i have miswritten the question, i'll retry:

    if f(x)=1/x
    evaluate
    [f(x)-f(a)]/(x-a)

    and the answer is supposed to be: -1/ax
    \frac{\frac{1}{x} - \frac{1}{a}}{x-a}

    get a common denominator for the two terms in the numerator and combine into a single fraction ...

    \frac{\frac{a-x}{ax}}{x-a}

    now finish it
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  6. #6
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    thank you, thats the step i got up to:

    <br /> <br />
\frac{\frac{a-x}{ax}}{x-a}<br />

    and i continued as follows, correct me if i am wrong:
     \frac{a-x}{ax*(x-a)}
    expanding:
    \frac{a-x}{ax(sqr)-a(sqr)x}

    and here is where i get stuck, don't know how to continue or simply that, thanks again
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  7. #7
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    Quote Originally Posted by str33tl0rd View Post
    thank you, thats the step i got up to:

    <br /> <br />
\frac{\frac{a-x}{ax}}{x-a}<br />

    and i continued as follows, correct me if i am wrong:
     \frac{a-x}{ax*(x-a)}

    do not \to expand

    now, what does \textcolor{red}{\frac{a-x}{x-a}} = ???
    ...
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  8. #8
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    thank you very much...
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