Question

How do you find the inverse of `f(x)=6x`?

Answer 1

`g(x)=x/6` is the inverse of `f(x)=6x`

Explanation:

`g(x)` is the inverse of `f(x)` if `f(g(x))=x` for all `x`

If `f(color(blue)x)=6color(blue)x`
then
`color(white)("XXX")f(color(blue)(g(color(red)x)))=6 * color(blue)(g(color(red)x))`
and if
`color(white)("XXX")6 * color(blue)g(color(red)x)=x`
then
`color(white)("XXX")color(blue)(g(color(red)x))=x/6`