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About. Transcript. 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.
- Set Notation
- Inequalities
- Interval Notation
Set notation takes the following form: As indicated by the figure, the above symbols read as "x is an element of the real numbers such that x is greater than two." In other words, x can be any real number as long as it is greater than 2. This is typically how set notation is used in the context of functions and real numbers; we start by stating tha...
Another way to specify the domain of a function is through use of inequalities (>, <, ≥, ≤). Depending on the complexity of the function, this may be done using a single inequality, or as a combination of multiple inequalities that describe which x values the function can take on.
Interval notation is used to describe intervals using parentheses and brackets, where parentheses represent an open interval while brackets represent a closed interval. An open interval is one that does not include the end values, while a closed interval is one that does. For example, the interval (11, 27), referred to as an open interval, indicate...
The range also excludes negative numbers because the square root of a positive number x is defined to be positive, even though the square of the negative number − √x also gives us x. Figure 3.3.20: Cube root function f(x) = 3√x. For the cube root function f(x) = 3√x, the domain and range include all real numbers.
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Domain and Range from Graphs. We can also talk about domain and range based on graphs. Since domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the graph. Remember that input values are almost always shown along the horizontal axis of the graph.
How To. Given the formula for a function, determine the domain and range. Exclude from the domain any input values that result in division by zero. Exclude from the domain any input values that have nonreal (or undefined) number outputs. Use the valid input values to determine the range of the output values.
Domain definition. The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs. For example, when we use the function notation f:R →R f: R → R, we mean that f f is a ...
So for this function, exactly the way it's written, it's not going to be defined with x is equal to 9 or x is equal to negative 10. So once again if you want a fan -- write in our fancy domain set notation. The domain is going to be x all the x's that are a member of the real such that x does not equal 9 and x does not equal negative 10.
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