Domain of a Function

Domain of a Function

The domain of a function is the set of all possible input values (x-values) that can be plugged into the function.

Key Characteristics:

• The domain is the set of all values for which the function is defined.
• It is the set of input values for which the function produces a valid output.
• The domain can be expressed using set notation, interval notation, or inequality notation.

Finding the Domain:

• To find the domain, look for values of x that make the function undefined.
• Identify any values of x that:
  • Make the denominator of a fraction equal to zero.
  • Make the expression inside a square root negative.
  • Make the expression inside a logarithm less than or equal to zero.
• Exclude these values from the domain.

Examples:

• The domain of f(x) = 1/x is all real numbers except x = 0, because dividing by zero is undefined.
• The domain of f(x) = √x is all non-negative real numbers, because the expression inside the square root cannot be negative.

Importance of Domain:

• The domain is crucial in determining the function's behavior and properties.
• It helps in identifying the range of the function.
• It is essential in solving problems and modeling real-world situations using functions.

Domain of a Function

• The domain is the set of all possible input values (x-values) that can be plugged into the function, producing a valid output.
• It can be expressed using set notation, interval notation, or inequality notation.

Key Characteristics of Domain

• The domain is the set of all values for which the function is defined.
• It is essential in determining the function's behavior and properties.

Finding the Domain

• Identify values of x that make the function undefined, such as:
  • Values that make the denominator of a fraction equal to zero.
  • Values that make the expression inside a square root negative.
  • Values that make the expression inside a logarithm less than or equal to zero.
• Exclude these values from the domain.

Examples

• The domain of f(x) = 1/x is all real numbers except x = 0, because dividing by zero is undefined.
• The domain of f(x) = √x is all non-negative real numbers, because the expression inside the square root cannot be negative.

Importance of Domain

• The domain helps in identifying the range of the function.
• It is essential in solving problems and modeling real-world situations using functions.