Question

Let y=f(x)=(3x+7)/(x-2)
find a rule for f^-1

Answer 1

`f^(-1)(x)=(2x+7)/(x-3)`.

Explanation:

The given function is
`f(x)=(3x+7)/(x-2),\:x\\e2`.

We want to find a rule for
`f^(-1)(x)`.

Let
`y=(3x+7)/(x-2)`.

Interchange x and y.

`x=(3y+7)/(y-2)`.

Solve for y.

`x(y-2)=3y+7`.

Expand

`xy-2x=3y+7`.

Group y-terms

`xy-3y=7+2x`.

Factor

`(x-3)y=7+2x`.

`y=(2x+7)/(x-3)`.

`\therefore f^(-1)(x)=(2x+7)/(x-3),\:x\\e3`.