Question

What would be the domain and range of y=(x-3)^2+2 and the domain and range of its inverse?

Answer 1

a parabola

Answer 2

Yep - and the vertex is at (3, 2), right?

Answer 3

For any polynomial, the domain is all real numbers. In interval notation, this looks like
(-infinity, infinity)

Now all we need to do is find the range.

Answer 4

The graph looks something like this.
So the range is [3, infinity)

Answer 5

Oops, [2, infinity)

Answer 6

ok

Answer 7

However, we are asked for the domain and range of the inverse, which means we need to switch the domain and range.
D: [2, infinity)
R: (-infinity, infinity)

Answer 8

*Technically, this function doesn't have an inverse, because it isn't 1-1

Answer 9

The most correct thing you could say is that the domain is [2, infinity) and the range is (-infinity, infinity), and that the function doesn't have an inverse.

If you had an invertible function, you could switch the domain and range (because you are just switching x and y)