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Domain → Function → Range. Example: when the function f (x) = x 2 is given the values x = {1,2,3,...} then those values are the domain. Domain, Range and Codomain. Illustrated definition of Domain of a Function: All the values that go into a function. The output values are called the range.
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.
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- I really didn't get the x€R thing. It didn't make any sense. We already covered this in school and i...The ϵ is the Greek letter epsilon. In this context epsilon is a symbolic way of saying "member of", so when you see "x ϵ" it means "x is a member o...
- Sal says that g(y) = (y-6)^1/2. Let y be 15. (15-6)^1/2 (9)^1/2 or +3 or -3. But as per definition c...Good question. When dealing with a square root function, we only consider the principal root (the positive root).
- If division by zero is undefined,then wouldn't the square root of zero also be undefined??In your ex...Division by zero IS NOT defined because there's NO number that when multiplied by zero gives the original (non-zero) number that's being divided by...
- I'm still confused, how do you know if the domain or range is a real number?Any number in the coordinate plane is a real number.
- For the second example to the video, at approximately 4:19, I'm wondering why negatives aren't possi...the value of y has to be greater than or equal to 6, or else the number under the radical would become negative. As we know, the square root of a n...
- What are the definitions of real numbers?The type of number we normally use, such as 1, 15.82, −0.1, 3/4, etc. Positive or negative, large or small, whole numbers or decimal numbers are al...
- Is the domain always the x-valueYes. If x is the input then the domain is x.
- G (y) =√ (y-6) has a sqr so it going to have 2 outputs, does it still being a function??When dealing with square root functions, we only deal with principal roots (meaning just the positive value).
- Why did Sal describe the function g(y) in terms of real numbers? I mean that we do know about comple...Functions are defined within the real number system as this is what is used the majority of the time. We graph functions within the coordinate plan...
- This concept makes sense to me when Sal does it with smaller numbers but I'm having trouble with a s...g(x) = (x + 1) / (x^2 - 2x - 15) The function will be defined for all real numbers except when the denominator equals 0. (We cannot divide by 0 aft...
The domain of a function includes all real input values that would not cause us to attempt an undefined mathematical operation, such as dividing by zero or taking the square root of a negative number. The domain of a function can be determined by listing the input values of a set of ordered pairs.
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by or , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be". [1] More precisely, given a function , the domain of f is X.
The domain and range of a function is all the possible values of the independent variable, x, for which y is defined. The range of a function is all the possible values of the dependent variable y.
Domain: The function. f(x) = x 2 + 2 . is defined for all real values of x (because there are no restrictions on the value of x). Hence, the domain of `f(x)` is "all real values of x". Range: Since x 2 is never negative, x 2 + 2 is never less than `2` Hence, the range of `f(x)` is "all real numbers `f(x) ≥ 2`".
When we identify limitations on the inputs and outputs of a function, we are determining the domain and range of the function. Definitions: Domain and Range. Domain: The set of possible input values to a function. Range: The set of possible output values of a function.
