In mathematics, the domain of a function refers to the set of all possible input values (usually represented as ‘x’) for which the function is defined. It is a crucial concept in understanding how functions work, as it specifies the range of values that can be fed into the function to obtain valid outputs.
Key Points About Domain
- The domain can include all real numbers, a specific range of numbers, or individual numbers, depending on the function.
- In some cases, the domain is restricted by the nature of the function. For example, a function involving a square root requires its input to be non-negative, as square roots of negative numbers are not real numbers.
- When graphing, the domain represents the set of x-values for which there are corresponding points on the graph.
Examples of Domains
Example 1: For a polynomial function like f(x) = x² – 5x + 6, the domain is all real numbers, as a polynomial is defined for every real number.
Example 2: For a function with a square root, like f(x) = √(x – 3), the domain is limited to x-values that make the expression under the square root non-negative. So, in this case, the domain is x ≥ 3.
Example 3: For a rational function like f(x) = 1 / (x – 2), the domain excludes values that would make the denominator zero. Hence, the domain is all real numbers except x = 2.
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