Inverse Functions

Sol 1 Let . Then , so and therefore .

Sol 2 Let . Then , so and . Thus .

Sol 3 Let , so and . Then , so . The domain of is the same as the range of , so it is the interval

since the graph of f is the top half of the parabola .

Sol 4 Let . Then , so

Sol 5 Setting , for example, and then solving for gives ; so is not 1-1 and therefore does not have an inverse.

Sol 6 Let ; then , so adding 4 to both sides gives and therefore . Taking square roots of both sides, using the fact that so , gives and so . Therefore . The domain of is the range of , which is the interval since for .

Sol 7 To find , we must solve the equation for :

since . Therefore .

Sol 8 Let .

Then

,

so .

The domain of is the same as the range of . Since for , for . Furthermore, if , then and therefore ; so the domain of is ,the range of .