Answer:
[tex](x+8)^2=y;\ x\ge -8[/tex]
Step-by-step explanation:
So the inverse is when the x and y are swapped
Original equation:
[tex]y=\sqrt{x}-8[/tex]
Swap x and y:
[tex]x=\sqrt{y}-8[/tex]
add 8 to both equations:
[tex]x+8=\sqrt{y}[/tex]
Square both sides
[tex](x+8)^2=y[/tex]
Now while this looks like a normal quadratic, it has to have the range restriction the original function had, but as it's domain restriction. So the range of the original function was y >= -8, because the smallest value you could input is 0, and the square root of that is 0, then subtract 8 and you get -8. So the domain is x >= -8
