Question

What is the inverse function of `f(x)=(2x+5)/(5x-3)`?

Answer 1

`f^(-1)(x) = (3x+5)/(5x-2)`

Explanation:

For ease of manipulation replace `f(x)` with `y`

`y = (2x+5)/(5x-3)`

`rarrcolor(white)("XX")5xy-3y = 2x+5`

`rarrcolor(white)("XX")5xy-2x=3y+5`

`rarrcolor(white)("XX")x(5y-2) = 3y+5`

provided `5y-2!=0`
`rarrcolor(white)("XX")x=(3y+5)/(5y-2)`

For the inverse function (which I will write as `f^(-1)(x)`) exchange the `x` and `y` variables, then replace `y` with `f^(-1)(x)`

`rarrcolor(white)("XX")f^(-1)(x) = (3x+5)/(5x-2)`