Question

Given g(x) = 2x/x-2, x≠2. find g¹³(8)​

Answer 1

8/3

Explanation:

`g^2 (x)=(2\left((2x)/(x-2) \right))/((2x)/(x-2)-2) \\ \\ =(4x)/(2x-2(x-2)) \\ \\ =(4x)/(4) \\ \\ =x`

From this, we can see that g(x) is its own inverse. Thus,
`g^(13)(x)=g(x)`

So,

`g^(13)(8)=(2(8))/(8-2)=8/3`