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Math Help - inverse function

  1. #1
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    inverse function

    i wonder how i what the inverse function to f(x) = 2x - 3-| x - 3 | looks lika and how I salve it
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  2. #2
    Senior Member abhishekkgp's Avatar
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    consider two cases, viz x>=3 and x<3.
    now check whether f(x) is bijection. if it is then inverse exists.
    after that find the inverse of each "piece".
    sketching the graph may also help.
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  3. #3
    MHF Contributor chisigma's Avatar
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    For 0 \le x \le 3 is y=3\ (x-2) that has as inverse \displaystyle x= \frac{y}{3}+ 2 ...

    Kind regards

    \chi \sigma
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  4. #4
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by chisigma View Post
    For 0 \le x \le 3 is f(x)=x that has as inverse itself...

    Kind regards

    \chi \sigma
    will not that be the case when x>=3??
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  5. #5
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    For x\le 3 (I don't see any reason to include the " 0\le x")
    x- 3< 0 so |x- 3|= -(x-3). Then f(x)= 2x- 3- |x- 3|= 2x- 3+ (x- 3)= 3x- 6 so that f^{-1}(x)= \frac{x+ 6}{3}= \frac{x}{3}+ 2 as chi-sigma said.

    For x\ge 3, |x- 3|= x- 3 so that
    f(x)= 2x - 3-| x - 3 |= 2x- 3- (x- 3)= x which has inverse f(x)= x.

    Of course, neither of those answers the question "what is the inverse of ?"
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  6. #6
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    so the function have tvo inverses ?
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