Question

Help pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

See below.

Explanation:

a.

`f(x) = (x + 12)/(x - 4)`

`y = (x + 12)/(x - 4)`

`x = (y + 12)/(y - 4)`

`x(y - 4) = y + 12`

`xy - 4x - y = 12`

`y(x - 1) = 4x + 12`

`y = (4x + 12)/(x - 1)`

`f^(-1)(x) = (4x + 12)/(x - 1)`

b.

`f(f^(-1)(x)) =`

`= ((4x + 12)/(x - 1) + 12)/((4x + 12)/(x - 1) - 4) =`

`= (((4x + 12)/(x - 1) + 12)(x - 1))/(((4x + 12)/(x - 1) - 4)(x - 1))`

`= (4x + 12 + 12x - 12)/(4x + 12 - 4x + 4)`

`= (16x)/(16)`

`= x`

`f^(-1)(f(x)) =`

`= (4((x + 12)/(x - 4)) + 12)/((x + 12)/(x - 4) - 1)`

`=([4((x + 12)/(x - 4)) + 12](x - 4))/(((x + 12)/(x - 4) - 1)(x - 4))`

`=(4x + 48 + 12x - 48)/(x + 12 - x + 4)`

`= (16x)/(16)`

`= x`