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Math Help - Inverse functions with ln and log

  1. #1
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    Inverse functions with ln and log

    1. I could use some guidance with a question that says "Find f^-1(3)"

    Given: F(x)= 3 + x^2 + tan(PIx/2), where -1 < x < 1

    I know I should find the inverse first then plug in 3 and solve. I just cannot get the inverse...

    First swap x and y, but after that I cannot think of how to isolate y. I have...
    x = 3 + y^2 + tan(PIy/2)

    Same problem thing with

    2. y = 3 + x + e^x find g^-1(4)
    what is "e" just a normal variable? The book says the answer is zero...

    Thanks a bunch!

    Tjvelcro
    Last edited by Tjvelcro; June 1st 2010 at 08:44 AM. Reason: Typos
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  2. #2
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    Quote Originally Posted by Tjvelcro View Post
    I could use some guidance with that says "Find f^-1(3)"

    Given: F(x)= 3 + x^2 + tan(PIx/2), where -1 > x > 1

    I know I should find the inverse first then plug in 3 and solve. I just cannot get the inverse...

    First swap x and y, but after that I cannot think of how to isolate y. I have...
    x = 3 + y^2 + tan(PIy/2)

    Same problem thing with

    y = 3 + x + e^x

    what is "e" just a normal variable? The book says the answer is zero...

    Thanks a bunch!

    Tjvelcro
    I assume you meant -1 < x < 1, since clearly we can't have -1 > 1.

    Maybe this isn't the answer you're looking for, but it's not extremely hard to recognize that plugging in x = 0 results in f(0) = 3, thus f^{-1}(3) = 0. Sometimes it's easier to recognize things than to solve methodically..
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