Answer:
[tex]g'(n) = -\frac{n+1}{3}[/tex]
Step-by-step explanation:
Given
[tex]g(n) = -3n - 1[/tex]
Required
Determine the inverse
[tex]g(n) = -3n - 1[/tex]
Replace g(n) with y
[tex]y = -3n - 1[/tex]
Swap positions of x and y
[tex]n = -3y - 1[/tex]
Make y the subject
[tex]3y = -n - 1[/tex]
[tex]3y = -(n + 1)[/tex]
[tex]y = -\frac{n+1}{3}[/tex]
Replace y with g'(n)
[tex]g'(n) = -\frac{n+1}{3}[/tex]
