Question

If f(x)=2x/x-5 find f^-1(x)

Answer 1

Look into the image. I hope it helps❤

#CarryOnLearning

Answer 2

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

Explanation:

let y = f(x) and rearrange making x the subject

y =
`(2x)/(x-5)` ( multiply both sides by x - 5 )

y(x - 5) = 2x ← distribute left side

xy - 5y = 2x ( subtract 2x from both sides )

xy - 2x - 5y = 0 ( add 5y to both sides )

xy - 2x = 5y ← factor out x from each term on the left side )

x(y - 2) - 5y ← divide both sides by y - 2

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

Change y back into terms of x with x =
`f^(-1)` (x) , then

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