Math Problem Statement

What is the domain of the square root of (x + 81)

Solution

To find the domain of the function f(x)=x+81f(x) = \sqrt{x + 81}, we need to consider the restriction that arises from the square root.

The square root function is only defined for non-negative numbers. This means the expression inside the square root, x+81x + 81, must be greater than or equal to zero:

x+810x + 81 \geq 0

Now, solve for xx:

x81x \geq -81

Thus, the domain of the function f(x)=x+81f(x) = \sqrt{x + 81} is all real numbers xx such that x81x \geq -81. In interval notation, the domain is:

[81,)[-81, \infty)

Summary:

  • The domain of x+81\sqrt{x + 81} is x81x \geq -81, or [81,)[-81, \infty).

Would you like further details on how to find domains for other functions or any related concepts? Here are some questions you might find helpful:

  1. How do you find the domain of a rational function?
  2. What happens when the expression inside a square root is negative?
  3. How do you find the domain of a function involving a fraction with a variable in the denominator?
  4. What is the domain of the function f(x)=1x+3f(x) = \frac{1}{x+3}?
  5. How can you find the range of a square root function?

Tip: When dealing with square roots, always ensure that the expression inside the square root is non-negative to avoid complex numbers in real-valued functions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Square Roots
Inequalities

Formulas

f(x) = √(x + 81)
x + 81 ≥ 0

Theorems

Domain of square root functions

Suitable Grade Level

Grades 8-10