Find b so g(x) = 1-x² has an inverse on [b,2]

[t_n_p]

Homework Statement

Let g:[b,2] -> R where g(x) = 1-x². If b is the smallest real value such that g has an inverse function, find b and g inverse

The Attempt at a Solution

I can find the inverse function easily, but I don't understand how I go about finding b.

According to the book, answer is b=0

 

[eumyang]

I would just look at the graph. Start by graphing g(x) = 1-x² with the restriction g:[-∞,2] -> R, and then look to see how much of the right portion of the graph is needed to make g(x) one-to-one.

 

[t_n_p]

right that makes sense!

In other words you can only take the inverse of a function f, if the original function f is one-to-one.

got it.