Domain of f(x) = 1/x + 5

Step by step

The question

Question: find the domain of f(x) = 1/x, + 5.

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 can never be 0.

The bottom is just x.

So x = 0 makes it 0.

So the domain is all real numbers except 0: x ≠ 0.

2 See it on the graph

Draw the grid.

Here is the graph of f(x) = 1/x, + 5.

It never touches x = 0: that x can't go in.

3 Check

Let's check.

Put 0 in: the bottom is 0.

Not allowed.

Let's look back.

First: find where the bottom is 0.

Then: see it on the graph.

Last: check.