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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- January 31st 2011, 09:56 AMpaulaainverse function
i wonder how i what the inverse function to f(x) = 2x - 3-| x - 3 | looks lika and how I salve it :)

- January 31st 2011, 09:58 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. - January 31st 2011, 10:11 AMchisigma
For is that has as inverse ...

Kind regards

- January 31st 2011, 10:13 AMabhishekkgp
- January 31st 2011, 11:44 AMHallsofIvy
For (I don't see any reason to include the " ")

x- 3< 0 so |x- 3|= -(x-3). Then f(x)= 2x- 3- |x- 3|= 2x- 3+ (x- 3)= 3x- 6 so that as chi-sigma said.

For , |x- 3|= x- 3 so that

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

Of course, neither of those answers the question "what is the inverse of ?" - January 31st 2011, 03:27 PMpaulaa
so the function have tvo inverses ?