domain
In mathematics, the term “domain” refers to the set of possible input values of a function
In mathematics, the term “domain” refers to the set of possible input values of a function. It represents all the values for which the function is defined.
To determine the domain of a function, you need to consider any restrictions or limitations on the input values. There are a few common types of restrictions to be aware of:
1. Radical Functions: Functions that include square roots or other radicals have a domain restricted by the requirement that the radicand (the expression inside the radical) must be non-negative. For example, the domain of the function f(x) = √(x) is all non-negative real numbers or x ≥ 0.
2. Rational Functions: Functions that involve ratios of polynomials may have restrictions based on the denominator. In general, the domain of a rational function is all real numbers except for the values that would make the denominator equal to zero. For example, for the function f(x) = 1/(x-2), the domain is all real numbers except x = 2.
3. Logarithmic Functions: Logarithmic functions have a domain defined by the requirement that the argument of the logarithm must be positive. For example, the function f(x) = log(x) has a domain of x > 0.
4. Exponential Functions: Similarly to logarithmic functions, exponential functions have a domain defined by the requirement that the base raised to the exponent is positive. For example, the function f(x) = 2^x has a domain of all real numbers.
5. Piecewise Functions: Piecewise functions are functions defined with different rules for different intervals of the domain. In this case, you need to identify the domains corresponding to each rule separately.
It’s important to carefully analyze the given function to identify any potential restrictions on the domain. Once you have determined the restrictions, you can write them as inequalities or intervals to represent the domain.
Note that the domain of a function is different from the range, which represents the set of possible output values.
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