# How do you write the inverse of the function y=x-12?

Jun 23, 2016

$x = y + 12$.

#### Explanation:

A function is a relationship between two variables.

For example your function is $y = x - 12$.
It means that if I give a number to $x$ I obtain a number for $y$.
Let's try:

if $x$ is $23$, $y$ is $y = 23 - 12 = 11$.

When you invert the function you want to invert the relationship between the two variables. You insert a value for $y$ and you get the value of $x$.

Let's try: if $y = 24$, what is $x$?

The relationship is

$24 = x - 12$.

We can solve this adding $12$ on both sides

$24 + 12 = x - \setminus \cancel{12} + \cancel{12}$

$36 = x$.

It seems that the inversion was done adding 12 on both sides.
We can generalize this to the initial equation

$y = x - 12$

if we add 12 on both sides we have

$y + 12 = x - \cancel{12} + \cancel{12}$

$y + 12 = x$.

This relationship tell us that for each value we assign to $y$ we obtain the value of $x$. That is exactly the inverse of the original function.