Question

Find the domain of each function. $$f(x)=\ln \left(x^{2}-9\right)$$

   Find the domain of each function.
$$f(x)=\ln \left(x^{2}-9\right)$$

Calculus with Applications

Calculus with Applications

Margaret L. Lial •… 11th Edition

Chapter 2, Problem 70

Instant Answer

Solved by Expert Sid Wan

05/19/2019

Step 1

The argument of the logarithm, $x^{2}-9$, must be greater than 0 because the logarithm is only defined for positive numbers. Show more…

Show all steps

lock

Thanks for your feedback!

Find the domain of each function. $$f(x)=\ln \left(x^{2}-9\right)$$

Play audio

Feedback

Powered by NumerAI

Sid Wan and 70 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Domain of a Function

The domain of a function is the set of all input values for which the function is defined. When determining the domain, one must consider any restrictions imposed by the mathematical operations involved, such as division by zero or taking the logarithm of a non-positive number.

Logarithmic Function Restrictions

A logarithmic function, such as the natural logarithm, requires its argument to be strictly positive. This means that for any function expressed as ln(g(x)), the condition g(x) > 0 must be satisfied in order for the output to be real.

Solving Quadratic Inequalities

When the argument of the logarithm is a quadratic expression, finding the domain involves solving a quadratic inequality. This typically includes factoring the quadratic, determining the critical points, and testing the intervals to identify where the inequality holds true.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later