Find the derivative of where and ,

Hence show that is a one-one function

I have found the derivative of h(x) to be but am confused on how i could use this to show is one-one

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- May 30th 2011, 02:54 AMPunchOne-one function
Find the derivative of where and ,

Hence show that is a one-one function

I have found the derivative of h(x) to be but am confused on how i could use this to show is one-one - May 30th 2011, 03:08 AMHallsofIvy
If a function is either always increasing or always decreasing then it is one to one,

- May 30th 2011, 03:23 AMPunch
oh... so u mean that the gradient is always decreasing or increasing, then it is one to one?

- May 30th 2011, 04:01 AMPunch
- Jun 4th 2011, 05:11 PMHallsofIvy
Do you understand what "one to one" means? A function, f, is one to one if and only if f(x)= f(y) implies x= y. If f is increasing, we can use "proof by contradiction": Suppose f(x)= f(y) with . Then either x> y so that f(x)> f(y) or x< y f(x)< f(y), either contradicting f(x)= f(y). The same argument works if f is decreasing.

- Jun 4th 2011, 05:13 PMHallsofIvy
- Jun 4th 2011, 05:25 PMAckbeet
- Jun 4th 2011, 08:49 PMCorpsecreate
For a function to be one-to-one, the function must pass the vertical line test and the horizontal line test for all values of x.