Question

Find the inverse of y=4-x/x​

Answer 1

Well if you do -4 on both sides you should get your answer, and you can do x on both sides but divide the number you get for y

Answer 2

`f^(-1) (x)`=
`(4)/(1+x)`

Explanation:

The first step is to switch y for x and x for y so the equation will look like

x=
`(4-y)/(y)`

the next thing you do is isolate y so you have to multiply y to both sides to get

`xy=4-y` now you got to add y to both sides which would get you

xy+y=4

since xy and y share a y value you have to try and factor out y which would get you

y(x+1)=4

the final step is to divide x+1 on both sides

y
`((x+1))/(x+1)`=
`(4)/(x+1)`

which since x+1 and x+1 crosses each other out we are left with

y=
`(4)/(1+x)`