Domain of f(x) = 6/x

Step by step

The question

Question: find the domain of f(x) = 6 over x.

The domain is all the x's we can put in.

1 Find where the bottom is 0

We can never divide by 0.

So the bottom of the fraction can never be 0.

The bottom is just x.

So x = 0 makes the bottom 0.

2 Write the domain

x = 0 is the only x that is not allowed.

The domain is all real numbers except 0: x ≠ 0.

3 Show it on a number line

Books also write the answer like this.

It is called interval notation.

A round bracket means the end is not in, like the open circle.

∞ means it goes on for ever.

∪ means or.

4 Check

Let's check.

Put 0 in: the bottom is 0.

Dividing by 0 is not allowed.

Now 1: the bottom is 1, not 0.

It works.

Let's look back.

First: find where the bottom is 0.

Then: write the domain.

Then: show it on a number line.

Last: check.