Answer:
Domain: All reals
Inverse: [tex]y = 1+\sqrt{2x+4}[/tex]
Step-by-step explanation:
To start, let's find the domain. Nothing is restricted, because (x-1)^2 is always defined, so it is the set of all reals. The inverse can be found by making the equation [tex]y = {1\over2}(x-1)^2-2[/tex], then switching all of the x's and y's and solving for y. We will get [tex]x = {1\over2}(y-1)^2-2\implies x+2={1\over2}(y-1)^2\implies 2x+4=(y-1)^2[/tex]. Now, take the square root of both sides and then add 1 to both sides to get [tex]y = 1+\sqrt{2x+4}[/tex].
