Question

How do you find the inverse of `f(x)=(2-3x)/4`?

Answer 1

`bar(f(x)) = (2-4x)/3`

Explanation:

If `bar(f(x))` is the inverse of `f(x)`
then, by definition of inverse, `f(bar(f(x))) = x`

Therefore
`f(bar(f(x))) = (2-3(bar(f(x))))/4 = x`

`2-3(bar(f(x)))=4x`

`-3(bar(f(x)))= 4x-2`

`bar(f(x)) = (2-4x)/3`

Answer 2

`f^-1(x)=-(4x-2)/3`

Explanation:

Rewrite as

`y=(2-3x)/4`

Flip the `x` and `y` and solve for `y`.

`x=(2-3y)/4`

Multiply both sides by `4`.

`4x=2-3y`

Subtract `2` from both sides.

`4x-2=-3y`

Divide both sides by `-3y`.

`-(4x-2)/3=y`

This can be rewritten in function notation, where `f^-1(x)` represents an inverse function.

`f^-1(x)=-(4x-2)/3`