Domain of f(x) = 1/(x^2 + 4)

Step by step

The question

Question: find the domain of f(x) = 1/(x² + 4).

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.

Which x makes x² + 4 zero?

A square is never below 0.

So x² + 4 is at least 4.

It is never 0.

No x makes the bottom 0.

So every x can go in: the domain is all real numbers.

2 Check

Let's check: x = 0 gives the smallest bottom, 4.

Not 0.

And x = 2: 8.

Never 0.

It works!

Let's look back.

First: find where the bottom is 0.

Last: check.