Question

is the inverse of f(x)= - √2(x+4) -8 (the 8 is not part of the square root)
this: (x+8/-1)^2/2 -4 (the 4 is not part of the fraction)

Answer 1

Y+8 = -sqrt ( 2x+8)
then
x +8 = -sqrt (2y+8)
(x+8)^2 = 2 y +8
2 y = (x+8)^2 - 8
y = (1/2)(x+8)^2 - 4
we disagree about the sign of -a*-a =+a

Answer 2

However, I will assume that 2(x+4) is all under the √
y = √(2(x+4)) - 8

step1 in finding the inverse: interchange the x and y variables

y = -√(2(x+4)) - 8 -----> x = -√(2(y+4)) - 8

step2, solve this new equation for y

x = -√(2(y+4)) - 8
x + 8 = -√(2(y+4))
square both sides
(x+8)^2 = 2(y+4)
( (x+8)^2 )/2 = y+4

y = ( (x+8)^2 )/2 - 4

However, in the original relation, we would have the restriction that
x ≥ -4 or else the result would not be a real number,
so in the inverse : y ≥ -4

not sure what x+8/-1 means in your answer of (x+8/-1)^2/2 -4
be careful with the brackets