Question

Inverse equation

1. g(n)= 2+(n+2)^3
2. f(n)= 1/2n+3/2

Answer 1

1

`g(n) = 2 + {(n + 2)}^(3)`

let the inverse be m :

`m = 2 + {(n + 2)}^(3) \\ {(n + 2)}^(3) = m - 2 \\ n + 2 = \sqrt[3]{(m - 2)} \\ n = \{ \sqrt[ 3]{(m - 2)} - 2 \}`

therefore:

`{ \boxed{ \boxed{g {}^( - 1)(n) = \{ \sqrt[3]{(n - 2)} - 2 \}}}}`

2.

`f(n) = (1)/(2) n + (3)/(2)`

let inverse be x :

`x = (1)/(2) n + (3)/(2) \\ \\ 2x = n + 3 \\ n = 2x - 3`

therefore:

`{ \boxed{ \boxed{f {}^( - 1)(n) = 2n - 3 }}}`