F⁻¹(x) stands for the invers of function f(x). The inverse of f(x) is equal to x. We need to solve for x.
solve for x
f(x) = 2x + 2
2x + 2 = f(x)
2x = f(x) - 2
x =

f⁻¹(x) =

Determine the value of f⁻¹(x) when x = 4
f⁻¹(x) =

f⁻¹(4) =

f⁻¹(4) =

f⁻¹(4) = 1
When x = 4, the value of f⁻¹(x) is equal to 1
I believe it is C because I think 0 is actually not an integer
Compairing g(x) with f(x), we can write:
To get g(x) f(x) is:
1) Multiplied by -1.
This implies the f(x) is reflected over x-axis
2) Addition of 4 to x
This implies f(x) is shifted 4 units to left
3) Subtraction of 2 to function value.
This implies f(x) is shifted down by 2 units.
So, we can write g(x) as:
g(x) = -f(x+4) - 2
So, the correct answer to this question is option A.
Shift 4 units left, reflect over x axis and shift 2 units down