Math Problem Statement

find function domain

Solution

To find the domain of a function, we need to determine all the possible input values (usually xx) for which the function is defined. Here's a general process to find the domain:

  1. Look for values that make the denominator zero (if the function involves a fraction).

    • The denominator cannot be zero because division by zero is undefined.
  2. Look for values that make the argument of a square root or any even root negative (if the function involves roots).

    • Square roots (or any even roots) are only defined for non-negative numbers.
  3. Check for values that make the logarithm argument zero or negative (if the function involves logarithms).

    • The logarithm is only defined for positive real numbers.

If you have a specific function in mind, please provide it, and I can help you find its domain.

Do you want a detailed explanation of how to identify the domain for a specific function?

Here are some related questions:

  1. How do you find the domain of a rational function?
  2. What is the domain of a square root function?
  3. Can a function have an infinite domain?
  4. How do you find the range of a function from its domain?
  5. What are some common mistakes people make when determining a function's domain?

Tip: Always consider restrictions like division by zero or square roots of negative numbers when determining the domain.

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Math Problem Analysis

Mathematical Concepts

Calculus
Algebra
Functions
Domain of a Function

Formulas

Domain restrictions: Denominator ≠ 0, argument of square root ≥ 0, logarithm argument > 0

Theorems

Domain of a rational function
Domain of square root function
Domain of logarithmic function

Suitable Grade Level

Grades 9-12