Question

#6 is the question, are these two functions inverse’s

Answer 1

I will find the inverse function of f(n) to see if it is g(n).


`f(n) = 2(n - 2)^3`


`y = 2(x - 2)^3`


`x = 2(y - 2)^3`


`(y - 2)^3 = (x)/(2)`


`y - 2 = \sqrt[3]{(x)/(2)}`


`y = \sqrt[3]{(x)/(2)} + 2`


`y = \sqrt[3]{ (x)/(2) } * \sqrt[3]{ (4)/(4)} + 2`


`y = \sqrt[3]{(4x)/(8)} + 2`


`y = \frac{ \sqrt[3]{4x }}{2} + 2`


`g(n) = \frac{\sqrt[3]{4n}} {2} + 2`

The inverse function of f(n) is indeed g(n), so f(n) and g(n) are inverse functions.