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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.
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.
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.
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.
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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