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).

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

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

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

$(y - 2)^3 = \dfrac{x}{2}$

$y - 2 = \sqrt[3]{\dfrac{x}{2}}$

$y = \sqrt[3]{\dfrac{x}{2}} + 2$

$y = \sqrt[3]{ \dfrac{x}{2} } \times \sqrt[3]{ \dfrac{4}{4}} + 2$

$y = \sqrt[3]{\dfrac{4x}{8}} + 2$

$y = \dfrac{ \sqrt[3]{4x }}{2} + 2$

$g(n) = \dfrac{\sqrt[3]{4n}} {2} + 2$

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