Find the inverse of:

1. g (x) = - 3 + 2

2. F (x) = - 2x^3

3. G (n) = 2n^3 - 2

4. g (x) = x^3

5. g (n) = - 1 - n^3

The inverse is found by first solving for the independent variable (in these questions, either x or n), then switching it with the dependent variable.

1. g (x) = - 3 + 2 = - 1

This function is simply a horizontal line (there is no presence of the independent variable x), so it has no inverse.

2. F (x) = - 2x^3

Solving for x: - F/2 = x^3

(-F/2) ^ (1/3) = x

Switch the variables to get the inverse function:

F (x) = (-x/2) ^ (1/3)

3. G (n) = 2n^3 - 2

G (n) + 2 = 2n^3

G (n) / 2 + 1 = n^3

n = [G (n) / 2 + 1]^ (1/3)

Inverse: G (n) = (n/2 + 1) ^ (1/3)

4. g (x) = x^3

[g (x) ]^ (1/3) = x

Inverse: g (x) = x^ (1/3)

5. g (n) = - 1 - n^3

g (n) + 1 = - n^3

-g (n) - 1 = n^3

[-g (n) - 1]^ (1/3) = n

Inverse: g (n) = (-n-1) ^ (1/3)