# Thread: Domain of a Variable

1. ## Domain of a Variable

I know that a variable is a letter for which we can substitute any number selected from a given set of numbers. The book tells me that the set of numbers is called the domain of the variable. Why is it call the domain of the variable? Is it safe to say that the idea of domain here the same as finding the domain of a function? I say no. Can someone explain the difference ?

2. ## Re: Domain of a Variable

I can just give you a variable $x$ and say it's domain is the naturals/integers/reals/complex numbers without any reference to a function.

On the other hand if I give you something like $f(x) = \sqrt{x}$ it's reasonable to say the domain of the variable $x$ is the non-negative real numbers where it's domain is driven by the nature of the function it's an argument of.

3. ## Re: Domain of a Variable

Originally Posted by romsek
I can just give you a variable $x$ and say it's domain is the naturals/integers/reals/complex numbers without any reference to a function.

On the other hand if I give you something like $f(x) = \sqrt{x}$ it's reasonable to say the domain of the variable $x$ is the non-negative real numbers where it's domain is driven by the nature of the function it's an argument of.
The domain of a function y = f(x) is the set of values that x can be so that the function is defined. The set of values that y can take is called the range.

4. ## Re: Domain of a Variable

Originally Posted by Debsta
The domain of a function y = f(x) is the set of values that x can be so that the function is defined. The set of values that y can take is called the range.
Thank you for including the range. The range is typically harder to find without a graph representation.