Use f(x) = 1 2 x and f -1(x) = 2x to solve the problems.
f−1(−2) =

f(−4) =

f(f−1(−2)) =

The answer to your question is below

Step-by-step explanation:

Functions

  f(x) = 12x           f⁻¹(x) = 2x

a)   f⁻¹(-2) = 2(-2)

     f⁻¹(-2) = -4

b) f(-4) = 12x

    f(-4) = 12(-4)

    f(-4) = -48

c) f(f⁻¹(-2)) =

   f(f⁻¹(x)) = 12(2x) = 24x

  f(f⁻¹(-2)) = 24(-2) = -48            

I think your functions are wrong they must be       f(x) = 1/2x    f⁻¹(x) = 2x        

a)  f⁻¹(-2) = 2(-2)

             = -4

b) f(-4) = 1/2(-4)

         = -2

c) f(f⁻¹(x)) = 1/2(2x)

              = x

  f(f⁻¹(-2)) = -2

Therefore, the 3rd graph represents the solutions to inequality.

Please also check the graph below.

Step-by-step explanation:

Given the expression

condition 1

Add 6 to both sides

Divide both sides by 2

condition 2

Add 6 to both sides

Divide both sides by 2

combine the intervals

Merging overlapping intervals

Thus,

Therefore, the 3rd graph represents the solutions to inequality.

Please also check the graph below.