PLEASE HELP ME OUT !!!!!!!! 20 POINTSSSSSS

Step One
For convenience f(x) = y
y = -(1/2) sqrt(x + 3)        Interchange x and y
x = -(1/2) sqrt(y + 3)        Multiply both sides by -2
(-2x) = sqrt(y + 3)            Square both sides
4x^2 = y + 3                     Subtract  3 from both sides
4x^2 -3 = y
f-1(x) = 4x^2  - 3 

Graphs
The original graph is in blue
The inverse is red.
Green Line y = x : explained below.

Comment
Inverses have a very strange property. It acts as a check.

If you perform the following operation
f-1(f(x)) you are left with x

In this case f-1[-1/2 sqrt(x + 3)]= 4(-1/2 * sqrt(x + 3))^2 - 3
f-1 (-1/2sqrt(x+3)) = 4 (1/4 (x+3) - 3
f-1(-1/2sqrt(x + 3)) = x+ 3 - 3 = x

I've included this because I think you have to put the same restriction on f-1(x) as you do on f(x) which is that for f(x) x ≥ -3

This last assertion could be incorrect, but I don't think so.
The answer is f-1(x) = 4x^2 - 3 <<<<< answer first box and
x≥-3 for the second box. <<<<<< answer for the second box.

Let me know if these are correct. I'm not sure about the restrictions.