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Math Help - Inverse Functions

  1. #1
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    Inverse Functions

    So, I need to find (F^-1)'(a) of

    f(x) = 3 x^2 + tan(πx/2) , -1< x < 1, a=3

    I have worked the problem to this point

    (f^-1)'(3) = 1/2x + sec^2(πx/2)π/2
    = 1/2(0) + sec^2(π(0)/2)π/2

    but my book and my professor tell me that the answer is 2/π, but I don't see how that can be. Shouldn't the answer be 1/0 because the 0's in the denominator give you 0 + 0, which is 0?
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  2. #2
    Junior Member frenzy's Avatar
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    Quote Originally Posted by zachb View Post
    So, I need to find (F^-1)'(a) of

    f(x) = 3 x^2 + tan(πx/2) , -1< x < 1, a=3

    I have worked the problem to this point

    (f^-1)'(3) = 1/2x + sec^2(πx/2)π/2
    = 1/2(0) + sec^2(π(0)/2)π/2

    but my book and my professor tell me that the answer is 2/π, but I don't see how that can be. Shouldn't the answer be 1/0 because the 0's in the denominator give you 0 + 0, which is 0?
    is f(x)=3*x^2 + tan(πx/2)

    or should it be

    f(x)=3+x^2 + tan(πx/2)
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  3. #3
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    yes it should be

    f(x)=3+x^2 + tan(πx/2)

    I'm trying to find (f^-1)'(a)

    so,

    1/f^-1(f^-1(a))= 1/2x + sec^2(πx/2)π/2
    1/2(0) + sec^2(π(0)/2)π/2

    I just want to know why the answer is 2/π.
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  4. #4
    Junior Member frenzy's Avatar
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    Quote Originally Posted by zachb View Post
    yes it should be

    f(x)=3+x^2 + tan(πx/2)

    I'm trying to find (f^-1)'(a)

    so,

    1/f^-1(f^-1(a))= 1/2x + sec^2(πx/2)π/2
    1/2(0) + sec^2(π(0)/2)π/2

    I just want to know why the answer is 2/π.
    f'(x)=2x+sec^2(nx/2)*(n/2)
    f'(0)=2(0)+sec^2(n0/2)*(n/2)=0+1*(n/2)=n/2

    f(0)=3 so f^{-1}(3)=0

    (f^{-1})'(3)=1/(f'(f^{-1}(3)))=1/f'(0)=1/(n/2)=2/n
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  5. #5
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    I guess what I should ask is why does n(0)/2 become n/2 instead of 0?
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  6. #6
    Junior Member frenzy's Avatar
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    Quote Originally Posted by zachb View Post
    I guess what I should ask is why does n(0)/2 become n/2 instead of 0?
    it doesn't

    n*0/2=0

    sec^2(n*0/2)=sec^2(0)=1

    so

    [sec^2(n*0/2)]*(n/2)=[1]*(n/2)=n/2
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