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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- Jan 31st 2011, 08:56 AMpaulaainverse function
i wonder how i what the inverse function to f(x) = 2x - 3-| x - 3 | looks lika and how I salve it :)

- Jan 31st 2011, 08:58 AMabhishekkgp
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. - Jan 31st 2011, 09:11 AMchisigma
For $\displaystyle 0 \le x \le 3$ is $\displaystyle y=3\ (x-2)$ that has as inverse $\displaystyle \displaystyle x= \frac{y}{3}+ 2$ ...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Jan 31st 2011, 09:13 AMabhishekkgp
- Jan 31st 2011, 10:44 AMHallsofIvy
For $\displaystyle x\le 3$ (I don't see any reason to include the "$\displaystyle 0\le x$")

x- 3< 0 so |x- 3|= -(x-3). Then f(x)= 2x- 3- |x- 3|= 2x- 3+ (x- 3)= 3x- 6 so that $\displaystyle f^{-1}(x)= \frac{x+ 6}{3}= \frac{x}{3}+ 2$ as chi-sigma said.

For $\displaystyle x\ge 3$, |x- 3|= x- 3 so that

f(x)= 2x - 3-| x - 3 |= 2x- 3- (x- 3)= x which has inverse $\displaystyle f(x)= x$.

Of course, neither of those answers the question "what is the inverse of ?" - Jan 31st 2011, 02:27 PMpaulaa
so the function have tvo inverses ?