# Inverse f(x)

1. Jan 19, 2010

### Monocerotis

1. The problem statement, all variables and given/known data

Find the inverse of each function. Is the inverse a function or a relation ?

f(x) = (x-4)/3

3. The attempt at a solution
Not sure which one is correct, and if any are not sure why (as in rules that may apply)

f(x) = (x-4)/3
f^-1(x) = 3x+4

or

f^-1 3x+12

2. Jan 19, 2010

### Fightfish

A way I usually approach such questions is by letting y = f(x), then making x the subject. Clearly then, the expression (in y) will give the inverse function.

Another way would be by observing that
$$f^{-1} (\frac{x - 4}{3}) = x = (\frac{x - 4}{3}) (3) + 4$$

You can always check the validity of your function by substituting test values.