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Math Help - Composite functions?

  1. #1
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    Composite functions?

    My first question is how would I multiply this

    (x^2+2(delta)x+delta(x)^2) (x+delta(x))

    My second questions is

    Evaluate the function at the given values of the independent variable.

    f(x)= 1/square root (x-1)

    f(x)-f(2)/(x-2)

    Can anyone show me how to do this one?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Composite functions?

    First question:
    Is delta a constant or? ...
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  3. #3
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    Re: Composite functions?

    My first question is how would I multiply this

    (x^2+2(delta)x+delta(x)^2) (x+delta(x))
    (x^2 + 2\delta(x) + {\delta}^2 (x))(x + \delta(x)) = x^3 + (2x + x^2)\delta(x) + (x+2){\delta}^2 (x) + {\delta}^3 (x)

    My second questions is

    Evaluate the function at the given values of the independent variable.

    f(x)= 1/square root (x-1)

    f(x)-f(2)/(x-2)
    f(x) = \frac{1}{\sqrt{x-1}}
    f(2) = 1
    f(x) - \frac{f(2)}{x-2} = \frac{1}{\sqrt{x-1}} - \frac{1}{x-2}

    Kalyan.
    Last edited by kalyanram; July 11th 2011 at 11:35 AM.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Composite functions?

    @kalyanram:
    Why do you calculate f(x-2)? I don't see that, just:
    f(x)-f(2)/(x-2) not f(x)-f(2)/f(x-2).

    Or do I miss something? ...
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  5. #5
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    Re: Composite functions?

    I am kind of confused when you get to the f(x-2)= 1/square root (x-3) part?
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  6. #6
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    Re: Composite functions?

    It would be far easier to start off by writing
    f(x)=\frac{1}{\sqrt{x-1}} as f(x)=\frac{\sqrt{x-1}}{x-1}.
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  7. #7
    Member kalyanram's Avatar
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    Re: Composite functions?

    Why do you calculate f(x-2)? I don't see that, just:
    f(x)-f(2)/(x-2) not f(x)-f(2)/f(x-2).

    Or do I miss something? ...
    That was a mistake indeed corrected it.
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  8. #8
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    Re: Composite functions?

    Dang it I think I used incorrect notation when writting this

    I meant

    (f(x)-f(2))/(x-2)
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: Composite functions?

    f(2) is already calculated by kalyanram so you just have to fill in ...
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  10. #10
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    Re: Composite functions?

    Well this is what I did

    I took Plato way of writing it

    square root(x-1)/(x-1)-(1/1)

    square root ((x-1)/(x-1)-(x-1)/(x-1))/((x-2)) I hope what I wrote makes sence
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  11. #11
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    Re: Composite functions?

    If f(x)=\frac{\sqrt{x-1}}{x-1} then f(2)=1.

    So \frac{f(x)-f(2)}{x-2}=\frac{\frac{\sqrt{x-1}}{x-1}-1}{x-2}
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  12. #12
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    Re: Composite functions?

    Hello, homeylova223!

    Evidently, these are from exercises involging Difference Quotients.


    How would I multiply this?

    . . \left(x^2+2\Delta x +[\Delta x]^2\right) (x+\Delta x)

    You are in PreCalculus or Calculus
    . . and you can't multiply polynomials?

    Hint: . (a+b)^3 \:=\:a^3 + 3a^2b + 3ab^2 + b^3




    Given: . f(x) \:=\: \frac{1}{\sqrt{x-1}}

    \text{Find: }\:\frac{f(x)-f(2)}{x-2}

    f(x) - f(2) \;=\;\frac{1}{\sqrt{x-1}} - \frac{1}{\sqrt{2-1}} \;=\;\frac{1}{\sqrt{x-1}} - 1 \;=\;\frac{1-\sqrt{x-1}}{x-1}

    \frac{f(x) - f(2)}{x-2} \;=\;\frac{1-\sqrt{x-1}}{(x-1)(x-2)}


    Rationalize the numerator:

    . . \frac{1-\sqrt{x-1}}{(x-1)(x-2)}\cdot\frac{1 + \sqrt{x-1}}{1 + \sqrt{x-1}} \;=\; \frac{1 - (x-1)}{(x-1)(x-2)(1 + \sqrt{x-1})}

    . . =\;\frac{2-x}{(x-1)(x-2)(1+\sqrt{x-1})} \;=\;\frac{-(x-2)}{(x-1)(x-2)(1+\sqrt{x-1})}

    . . =\;\frac{-1}{(x-1)(1+\sqrt{x-1})}

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  13. #13
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    Re: Composite functions?

    Your Algebra skills are supreme I could have never figured that out on my own!
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