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Math Help - Need help on natural logs

  1. #1
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    Need help on natural logs

    g(x) = ln sqrt (x+2)

    Find the value of g^-1 (0)
    How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by letzdiscuss View Post
    g(x) = ln sqrt (x+2)

    Find the value of g^-1 (0)
    How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks
    Here's one way:

    Let y=g(x)=\ln\sqrt{x+2}. To find the inverse, we swap x's and y's to get x=\ln\sqrt{x+2}. Now, we resolve the equation for y:

    x=\ln\sqrt{y+2}\implies e^x=\sqrt{y+2}\implies\dots\implies y=g^{-1}\left(x\right)=\dots.

    Then evaluate it at x=0.

    Can you take it from here?
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  3. #3
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    so to find the inverse you just switch the x and y and solve for y.

    So if you have g(x) = y = ln sqrt (x+2)

    you change it to x = ln sqrt (y+2) and solve for y:
    x^e = sqrt(y+2)
    x^2e = y+2

    etc.

    and if you want g inverse of 0, then you just plug in 0=x.

    edit: woops, a minute too late. haha.
    Last edited by kleo; September 19th 2009 at 10:04 PM.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by letzdiscuss View Post
    g(x) = ln sqrt (x+2)

    Find the value of g^-1 (0)
    How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks
    Start by letting g(x)=y and then switching x and y. Then solve for y.

    Ah! Beaten to the punch!
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  5. #5
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    Thanks everyone !!!! That helped a lot !!
    I really really appreciate it !
    Last edited by letzdiscuss; September 19th 2009 at 10:33 PM.
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  6. #6
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    Quote Originally Posted by letzdiscuss View Post
    g(x) = ln sqrt (x+2)

    Find the value of g^-1 (0)
    How would I start? I'm stuck on this question for hours ! Please give me some hints. Thanks
    Or, since you are only asked for g^{-1}(0), solve 0= ln(\sqrt{x+2}} for x. Taking the exponential of both sides, e^0= 1= \sqrt{x+2}. Squaring both sides, 1= x+2 so x= -1. That shows that g(-1)= 0 so g^{-1}(0)= -1.
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