Given f:x -> (x-1)(x-3), for x ≤ c. Find the largest possible value of c for which the inverse of f exists.

I have sketched the graphs for f and inverse of f but that seems not that helpful. Can anyone help me? Thank you...

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- May 26th 2011, 05:03 AMMichaelLightFunction
Given f:x -> (x-1)(x-3), for x ≤ c. Find the largest possible value of c for which the inverse of f exists.

I have sketched the graphs for f and inverse of f but that seems not that helpful. Can anyone help me? Thank you... - May 26th 2011, 05:16 AMjgv115
The question is asking you to restrict this quadratic so that it will have a inverse

*function*. For something to have an inverse function it needs to be a one to one function. So think about how you could make that quadratic into a one to one function because at the moment it is not as the graph has more than 1 x value for each y value - May 26th 2011, 06:52 AMHallsofIvy
$\displaystyle (x- 1)(x- 3)= x^2- 4x+ 3$. Can you find the

**vertex**of that parabola? That is where it turns up again and so is not "one to one".