Step-by-step explanation:
f(x) = y = -1/2 × sqrt(x + 3), x >= -3
-2y = sqrt(x + 3)
4y² = x + 3
x = 4y² - 3
and now we need to rename x to y and y to x to make it a "normal" function :
y = 4x² - 3
since in the original function x >= -3, this gave us y <=0.
and therefore (remember the x of the inverse function actually stands for the y of the original function) the limit for the inverse function is x <= 0.
so, again, the full answer is
f^-1(x) = 4x² - 3, x <= 0
