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Math Help - Solve this function

  1. #1
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    Solve this function

    Hey guys!
    2f(x)-3f(1/x)=x^2, x not = 0, find f(2). options are
    1. -7/4, 2.5/2, 3.-1, 4.none

    Please solve it asap...i'm unable to solve it........thanks
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  2. #2
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    plug in x=2 and x=1/2, you obtain system of two equations, easy to solve. answer is f(2)=-7/4.
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  3. #3
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    thanks......n another prob...

    thanks...tht helped a lot.......
    there is another question:
    f(x)=cos(log x) then find f(x)f(4)-1/2 ( f(x/4)+f(4x)). Options are:
    1,-1,0,1 &-1 both
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  4. #4
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    To work this you will need to know these facts.
    f\left( {\frac{x}{4}} \right) = \cos \left( {\log (x) - \log (4)} \right)\,\& \,f\left( {4x} \right) = \cos \left( {\log (x) + \log (4)} \right)
    \cos \left( {A - B} \right) + \cos \left( {A + B} \right) = 2\cos (A)\cos (B)

    You can put all that together, after all it is your problem.
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  5. #5
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    thanks...

    Thanks mr.plato.....i knew it's my prob.....u didn't need to tell me tht...i was expecting only what u send-"a hint".......

    nyways.....there is another question.....again i would appreciate a hint....

    f is a real valued function given by f(x)=27x^3+(1/x^3), and a,b are roots of 3x+(1/x)=12. Then
    1. f(a) not equal to f(b), 2.f(a)=10, 3.f(b)=-10, 4. none of these.
    Last edited by sapanjot; August 14th 2008 at 06:12 AM. Reason: math notations
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  6. #6
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    Well O.K., here is just a hint:
    27x^3  + \frac{1}{{x^3 }} = \left( {3x + \frac{1}{x}} \right)\left( {9x^2  - 3 + \frac{1}{{x^2 }}} \right)
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