Determine the domain of (√(x+5))/(√(x+5)). Explain how you |...

Name: Problem 121, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2020-09-01T03:13:29-08:00
Duration: 29 s
Channel: Amy Jiang
Description: Determine the domain of (√(x+5))/(√(x+5)). Explain how you

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Key Concepts

Domain of a Function

The domain of a function encompasses all the values for which the function is defined. When determining the domain, one must identify any restrictions, such as values that make a denominator zero or result in an undefined expression like the square root of a negative number.

Square Root Function

Square root functions require that the expression under the radical (the radicand) is nonnegative, because the square root of a negative number is not a real number. This leads to an inequality that must be solved to ensure that the radicand is greater than or equal to zero.

Cube Root Function

Cube root functions are defined for all real numbers, as taking the cube root of any real number, whether it is positive, negative, or zero, results in a real number. However, even though cube roots don't impose constraints on the domain by themselves, they may still appear in expressions with other restrictions.

Restrictions Due to Division

When a function includes a division, it is necessary to ensure that the denominator is never zero because division by zero is undefined. This means any value that makes the denominator equal to zero must be excluded from the domain.

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