Let's break down the given equation step by step.

1. Original equation: F(x) = 3/(x+2) = -12x

2. Applying function composition: [F∘g](x) = x

Now, we need to find the function g(x) such that [F∘g](x) = x.

To do this, we substitute [F∘g](x) into the original equation for F(x):

F([F∘g](x)) = 3/([F∘g](x) + 2) = -12[F∘g](x)

Substituting x for [F∘g](x) gives:

F(x) = 3/(x+2) = -12x

Now, let's solve this equation for x:

3/(x+2) = -12x

Multiply both sides by (x+2) to eliminate the denominator:

3 = -12x(x+2)

Expand the equation:

3 = -12x^2 - 24x

Rearrange the equation to bring all terms to one side:

12x^2 + 24x + 3 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 12, b = 24, and c = 3.

Substituting the values into the quadratic formula:

x = (-24 ± √(24^2 - 4*12*3)) / (2*12)

Simplifying the expression under the square root:

x = (-24 ± √(576 - 144)) / 24

x = (-24 ± √432) / 24

x = (-24 ± 20.784) / 24

This gives us two possible solutions:

x1 = (-24 + 20.784) / 24 ≈ -0.099

x2 = (-24 - 20.784) / 24 ≈ -1.574

Therefore, the function g(x) that satisfies [F∘g](x) = x is:

g(x) = -0.099 or g(x) = -1.574