Question

Let f(x)=2x+2. solve f^-1(x) when x=4

Answer 1

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.