Question
how to find the domain of a function
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The domain of a function is the complete set of possible values of the independent variable from the function; in other words, it's the set of all possible x-values which will make the function "work", and will output real y-values. Here is a basic method to find it:
1. Identify the function that has been given.
2. Look for any values that would make the function undefined or create a mathematical error (such as division by zero or taking the square root of a negative number).
3. Exclude these values from the possible values for x to find the domain.
For example, if you're looking for the domain of the function f(x) = 1/(x-3), the function would be undefined when x = 3, since you would be dividing by zero. Therefore, the domain is all real numbers except for x = 3.
If your function has a square root, such as f(x) = sqrt(x), the domain is all real numbers that make the value inside the square root zero or positive. Any negative value under a square root would result in an imaginary number which is not considered in this context, so for this function, the domain is x >= 0.
For a more complex function, consider all the rules (square roots, logarithms, fractions...) to exclude any values that could cause a problem. In some cases, you may end up with intervals.
Remember, the domain concerns x-values (horizontal/independent variable), not the y-values (vertical/dependent variable).
1. Identify the function that has been given.
2. Look for any values that would make the function undefined or create a mathematical error (such as division by zero or taking the square root of a negative number).
3. Exclude these values from the possible values for x to find the domain.
For example, if you're looking for the domain of the function f(x) = 1/(x-3), the function would be undefined when x = 3, since you would be dividing by zero. Therefore, the domain is all real numbers except for x = 3.
If your function has a square root, such as f(x) = sqrt(x), the domain is all real numbers that make the value inside the square root zero or positive. Any negative value under a square root would result in an imaginary number which is not considered in this context, so for this function, the domain is x >= 0.
For a more complex function, consider all the rules (square roots, logarithms, fractions...) to exclude any values that could cause a problem. In some cases, you may end up with intervals.
Remember, the domain concerns x-values (horizontal/independent variable), not the y-values (vertical/dependent variable).
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