You have to find the inverse of the function, then plug in -25 to that.
So:
First replace y with x and x with y
x=4(y+8)^2 - 9
Solve for y
x + 9 = 4(y+8)^2
(x + 9)/4 = (y+8)^2
Here square root both sides
sqrt((x + 9)/4) = y + 8
Subtract 8 from both sides
y = sqrt((x + 9)/4) - 8
Now plug in -25 in this equation
y = sqrt((-25 + 9)/4) - 8
solve
y = sqrt((-16 / 4)) - 8
Here, there is a negative number under the square root sign. So, -25 cannot be in the domain and the answer is D.