how to find the domain of a function?

Answer 1

To find the domain of a function, follow these steps:

1. Identify any restrictions or limitations on the function. For example, certain mathematical operations (such as division by zero or taking the square root of a negative number) may introduce restrictions.

2. Check for any specific instructions or conditions given in the problem or function definition. These may also limit the domain.

3. Determine if the function is defined for all real numbers, or if it is only defined for a specific subset of real numbers, such as positive numbers or integers.

4. Identify any excluded values by analyzing the function for potential restrictions. This can involve looking for denominators that cannot be equal to zero, square roots that must have a positive argument, or logarithms that must have a positive or non-zero argument.

5. Write down the domain of the function using interval notation. For example, if the function is defined for all real numbers except x = 5, the domain can be represented as (-∞, 5) ∪ (5, +∞).

Note: In some cases, the domain may be specified for you based on the context of the problem.