Question

F(x) =4 over x - 3

g(x) =x - 2 over x
(a) Express the inverse function f −1
in the form f ^-1 (x)

Answer 1

Explanation:

`f(x) = (4)/(x - 2) \\ g(x) = (x - 2)/(x)`

`{f}^( - 1) (x) ... \\ x = (4)/(y - 2) \\ y - 2 = (4)/(x) \\ {f}^( - 1) (x) = (4)/(x) + 2`

`{g}^( - 1) (x)... \\ x = (y - 2)/(y) \\ xy = y - 2 \\ xy - y = - 2 \\ y(x - 1) = - 2 \\ {g}^( - 1) (x) = ( - 2)/(x - 1)`