Math Problem Statement

Find the domain of the function f(x) = log(x - 16). Write your answer using interval notation.

Solution

To find the domain of the function f(x)=log(x16)f(x) = \log(x - 16), we need to identify where the argument inside the logarithm is positive.

For the logarithmic function log(x16)\log(x - 16) to be defined, the expression inside the logarithm must be greater than 0:

x16>0x - 16 > 0

Solving this inequality:

x>16x > 16

Thus, the domain of the function f(x)f(x) is all xx values greater than 16. In interval notation, this is written as:

(16,)(16, \infty)

Would you like further details on this solution or have any additional questions?

Here are some related questions to explore:

  1. What is the domain of f(x)=log(2x+3)f(x) = \log(2x + 3)?
  2. How does the base of the logarithm affect the domain of a function?
  3. What happens to the graph of f(x)=log(x16)f(x) = \log(x - 16) as xx approaches 16 from the right?
  4. Can the logarithm function ever be negative?
  5. How do you find the domain of a composition of functions involving logarithms?

Tip: Always remember that the argument of a logarithmic function must be strictly positive.

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Math Problem Analysis

Mathematical Concepts

Algebra
Logarithmic Functions

Formulas

Logarithmic Function Domain: log_b(x) is defined for x > 0

Theorems

Domain of Logarithmic Functions

Suitable Grade Level

Grades 9-12