Week 4 – Math 11 – Specifying Domain

When working with variable radicals, it’s important to show what that variable could possibly be. How we show this in math is by specifying the domain of the variable.

This is just a complicated way of saying that we find whether the variable is positive, negative, or either and we write it as so:

Positive –

Negative –

Either –

Now that we know how to write these, all we need to know now is how to put them to use. I’ll put an example of each and explain why I used each one.

;

The x here can only be positive because a number in an even root can only be positive. This is because a number multiplying by itself an even amount of times will always be positive.

Ex.

 

 

See?

 

;

The x here can only be negative because a number in an odd root will always have the same sign as whatever number the radicand is (positive, negative). This is because a number multiplying by itself an odd amount of times will always be the same sign as the original number.

Ex.

 

 

See?

 

;

The x here can be anything because even if square roots can only have positive numbers, since the radicand is being squared, it doesn’t matter because the radicand will always equal a positive.

Ex.

 

 

See?

 

There is also an exception to these 3, but since I didn’t mention it earlier, I’ll mention it here.

Sometimes a variable won’t be positive or negative.

Ex.

In this case we will just write

So…

;

 

Yeah that’s pretty much it.