Question

If `f(x) = 6x-4`, what is `f^-1(x)`?

Answer 1

Here it is.....

Explanation:

1. Let `f(x)=color(red)y` so that it is easily replacable

2. Then make `x` in terms of `y`

   `color(red)(y)=6color(blue)(x)-4`

   `6color(blue)(x)-4=color(red)(y)`

   `6color(blue)(x)=color(red)(y)+4`

   `color(blue)(x)=(color(red)(y)+4)-:6`

3. Replace the `color(blue)(x)` by `f^-1(x)` and replace the `color(red)(y)` by the `color(blue)(x)`

`f^-1(x)=(color(blue)(x)+4)-:6`