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Math Help - Functions Question 2

  1. #1
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    Exclamation Functions Question 2

    Given  f(x)=\frac{1}{x} .Find  \frac{f(x+h)+f(x)}{h} where h is not equal to zero

    Attempt:
     \frac{\frac{h}{x+h*x)}}{h}
    How to simplify (please provide steps)


    Thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Given  f(x)=\frac{1}{x} .Find  \frac{f(x+h)+f(x)}{h} where h is not equal to zero

    Attempt:
     \frac{\frac{h}{x+h*x)}}{h}
    How to simplify (please provide steps)


    Thank you
    \frac{\frac{1}{x+h}+\frac{1}{x}}{h}

    \frac{2x+h}{x^2+xh}\cdot \frac{1}{h}

     <br />
\frac{2x+h}{x^2h+xh^2}<br />
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  3. #3
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    Quote Originally Posted by mj.alawami View Post
    Given  f(x)=\frac{1}{x} .Find  \frac{f(x+h)+f(x)}{h} where h is not equal to zero
    you sure it's not  \frac{f(x+h)-f(x)}{h}
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  4. #4
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    Quote Originally Posted by skeeter View Post
    you sure it's not  \frac{f(x+h)-f(x)}{h}
    yes you are correct and i am wrong? So how is it done ?
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  5. #5
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    Quote Originally Posted by mj.alawami View Post
    Given  f(x)=\frac{1}{x} .Find  \frac{f(x+h)+f(x)}{h} where h is not equal to zero

    Attempt:
     \frac{\frac{h}{x+h*x)}}{h}
    How to simplify (please provide steps)


    Thank you
    f(x) = \frac{1}{x}


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


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

     = \frac{x}{x(x + h)} - \frac{x + h}{x(x + h)}

     = -\frac{h}{x(x + h)}


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

     = -\frac{h}{x(x + h)}\cdot\frac{1}{h}

     = -\frac{1}{x(x + h)}.
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  6. #6
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    Talking

    Quote Originally Posted by mj.alawami View Post
    So how is it done ?
    To learn, in general, how to evaluate a function at an expression (rather than a number), try here.

    Then try working this exercise in pieces, rather than all at one. First write down the formula for f(x). Then find the expression for f(x + h). Then subtract the polynomial for f(x) from the polynomial for f(x + h). Then divide by h, cancelling if you can.
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