Question

What is the domain of the inverse of the functiony = -2(x - 1)2 + 3?

Answer 1

The given function is

$y=-2(x-1)^2+3$

The inverse a function can be defined as the relation with the opposite domain and range sets. In other words, the range of the given function is the domain of its inverse.

To know the range of the given function we need to find the vertex (h,k). However, the given function is in vertex form

$y=a(x-h)^2+k$

This means

$h=1,k=3$

Now, the range is determined by k, because it's the limit condition of y-variable. So, we can deduct that the range is

$R\colon\left\lbrace x\in\R|x\leq3\right\rbrace$

As we said before, the range of the given function is the domain of its inverse, which are all real numbers less than or equal to 3.

Therefore, the right answer is the third choice.