Domain of a Function

So I know domain implies input, but how would one go about finding the domain of a problem such as this:

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Originally Posted by SHiFT

So I know domain implies input, but how would one go about finding the domain of a problem such as this:

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• The denominator must never equal 0
• Anything under a square root must be greater than or equal to 0

In this case

Quote:

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Originally Posted by SHiFT

So I know domain implies input, but how would one go about solving a problem such as this:

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Two things about functions such as this one: 1) it won't exist when there is a negative inside the square root and 2) it won't exist when you're dividing by zero.

Based on the first thing:

So

Based on the second thing, the denominator cannot be zero. Since the denominator is x,

The domain is all real numbers less than or equal to 1 except 0.

Thanks a lot guys, It's hard for me to understand a problem when I'm looking at it, but once I see the solution it makes so much sense.

If you get something like this, it's just anything in the denominator that's going to make it zero.

Since it was just plain old , you'd think about making it zero since any number you could possibly plug in would not make the denominator zero unless it was 0 itself.

This goes for anything like that pretty much.

Like take for instance:



What's gonna make it zero?

Well a negative and a positive squared is always going to end up positive and to make it zero what would you need to get make it that way? Well, you'd need some number squared to make 9. What number also though too because




Can't divide by zero.