Question

Find the inverse of:

Answer 1

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)