Question

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

Answer 1

`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-\cancel12+cancel12`

`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-cancel12+cancel12`

`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.