f⁻¹(x) is the notation for the inverse of an equation, so you just need to find the inverse equation. that's found by swapping your x and y variables:
f(x) = 2x + 2 ... replace f(x) with y
y = 2x + 2 ... swap x and y variables
x = 2y + 2 ... solve for y
x = 2y + 2 ... subtract 2
x - 2 = 2y ... divide by 2
(x - 2)/2 = y
so, f⁻¹(x) = (x - 2)/2 ... now you need to solve that for when x = 4. plug it in:
f⁻¹(x) = (4 - 2)/2 ... simplify the top of the fraction
f⁻¹(x) = 2/2
f⁻¹(x) = 1 is your answer.
