# How to write all real numbers domain

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Domain of a function Video transcript Let's have a little bit of a review of what a function is before we talk about what it means that what the domain of a function means. So function we can view as something -- so I put a function in this box here and it takes inputs, and for a given input, it's going to produce an output which we call f of x.

So, for example, let's say that we have the function -- let's say we have the function f of x is equal to 2 over x. So in this case if -- let me see -- that's my function f.

If I were to input the number 3. Well, f of 3 that we're going to output -- we have, we know how to figure that out. We've defined it right over here. It's going to be equal to 2 over 3.

So we're able, for that input, we're able to find an output. If our input was pi, then we input into our function and then f of pi -- when x is pi, we're going to output f of pi, which is equal to 2 over pi.

So we could write this as 2 over pi. We're able to find the output pretty easily.

But I want to do something interesting. Let's attempt to input 0 into the function. If we input 0 then the function tells us what we need to output. Does this definition tell us what we need to output? So if I attempt to put x equal 0, then this definition would say f of 0 be 2 over 0, but 2 over 0 is undefined.

Rewrite this -- 2 over 0. This function definition does not tell us what to actually do with 0.

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It gives us an undefined answer. So this function is not defined here. It gives a question mark. So this gets to the essence of what domain is.

## Introduction to the domain and range of a function

Domain is the set of all inputs over which the function is defined. So the domain of this function f would be all real numbers except for x equals 0.

So we write down these, these big ideas. This is the domain -- the domain of a function -- Actually let me write that out. The domain of a function A domain of a function is the set of all inputs -- inputs over which the function is defined -- over which the function is defined, or the function has defined outputs over which the function has defined outputs.

So the domain for this f in particular -- so the domain for this one -- if I want to say its domain, I could say, look, it's going to be the set of these curly brackets.

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These are kind of typical mathy set notation. I said OKit could be the set of -- I gonna put curly brackets like that. Well, x can be a member So this little symbol means a member of the real numbers.

But it can't be any real number.A complex number is a number of the form a + bi, where a and b are real numbers and i is an indeterminate satisfying i 2 = −alphabetnyc.com example, 2 + 3i is a complex number.

A complex number may therefore be defined as a polynomial in the single indeterminate i, with the relation i 2 + 1 = 0 imposed. From this definition, complex numbers can be added or multiplied, using the addition and.

The set of non-negative numbers is $$[0,\infty)$$. A subset of the number line consisting or two or more intervals is written using the set union symbol $$\cup$$. For example, the set of all real numbers lying at least one unit from $$0$$ but less than two units from zero written in interval notation is $$(-2,-1]\cup[1,2)$$.

Functions assign outputs to inputs. The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

## How to find the domain of a function (video) | Khan Academy

Interval notation is a method of writing down a set of numbers. Using interval notation we will show the set of number that includes all real numbers except 5. First, stated as inequalities this group looks like this: It is often used to state the set of numbers which make up the domain and range of .

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