Question

If `f(x) = (2x+5)/x`, what is `f^-1(x)`?

Answer 1

`f^-1(x)=\frac{5}{x-2}`

Explanation:

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

Let `y=(2x+5)/x`
Now solve `y=(2x+5)/x` for `y`
`yx=2x+5`
`yx-2x=5`
`x(y-2)=5`
`x=5/(y-2)`

So,
`x=f^-1((2x+5)/x)`
`5/(y-2)=f^-1(y)`
And
,`f^-1(x)=\frac{5}{x-2}`