Question

What is the inverse equation of the function, `y= 3x-6`?

Answer 1

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

Explanation:

Concept

`f^(-1)(x)` (inverse of `f(x)`) means to switch the `x` and `y` variables in the equation `f(x)`
This means `f^(-1)(x)=f(y)`

Solving

• Given function `f(x)=3x-6`, then `f^(-1)(x)\rArr\color(indianred)(x=3y-6)`
• We must isolate the `y` in `f^(-1)(x)` to get the proper form of the inverse.
  `x=3y-6`
  `x+6=3y`
  `x/\color(red)(3)+6/\color(red)(3)={\cancel(3)y}/\cancel(\color(red)(3))`
  `y=1/3x+2`

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