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