## domain of a function

### The domain of a function is the set of all possible input values for which the function is defined

The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of values that you can plug into the function to get meaningful output.

When determining the domain of a function, there are a few key considerations:

1. Real numbers: Most commonly, functions are defined over the set of real numbers, which includes all rational and irrational numbers. If a function is not specified otherwise, it is generally assumed that the domain is the set of all real numbers.

2. Excluded values: In some cases, certain values of the input variable are not allowed due to restrictions in the function. For example, a function might contain a square root, and the input cannot be a negative number since the square root of a negative number is not a real number. In such cases, the domain would exclude any values that cause these restrictions.

3. Division by zero: Another important consideration is the presence of fractions or rational expressions within the function. Division by zero is not defined, so any value that would result in division by zero must be excluded from the domain.

To find the domain of a function, you need to analyze these potential restrictions and determine all the values that are valid inputs. It is essential to understand the properties of the function and any limitations or specific conditions it may have.

For example, let’s consider the function f(x) = 1/x. In this case, we need to exclude the value x = 0 since division by zero is undefined. Therefore, the domain of this function would be all real numbers except 0.

However, let’s consider another function g(x) = √(x – 4). In this case, the square root is only defined for non-negative values, so x – 4 must be greater than or equal to 0. Solving this inequality, we find x ≥ 4. Therefore, the domain of g(x) would be all real numbers greater than or equal to 4.

In summary, the domain of a function represents the set of valid input values for which the function is defined, taking into account any restrictions or constraints specific to the function.

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