Question

How do you find the inverse of `f(x)=3x-5`?

Answer 1

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

Explanation:

`f(x)=3x-5`
The inverse of a function completely swaps the x and y values. One way to find the inverse of a function is to switch the "x" and "y" in a equation
`y=3x-5` turns into `x=3y-5`
Then solve the equation for y
`x=3y-5`
`x+5=3y`
`1/3x+5/3=y`
`f(x)^-1 =1/3x+5/3`

Answer 2

`f(x)=3x-5`

`y=3x-5`

`x=3y-5`

add three to both sides

`3y=x+5`

divide by `three` on both sides

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

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