Math Problem Statement

Let f(x) = ln(3 - x) + 2.

Solution

The image shows the function:

f(x)=ln(3x)+2f(x) = \ln(3 - x) + 2

Would you like assistance with differentiating, finding critical points, or analyzing the behavior of this function? Let me know how you'd like to proceed!

Here are some related questions:

  1. What is the domain of f(x)=ln(3x)+2f(x) = \ln(3 - x) + 2?
  2. How do you compute the derivative of f(x)=ln(3x)+2f(x) = \ln(3 - x) + 2?
  3. What are the critical points of f(x)f(x)?
  4. How do you find the range of f(x)f(x)?
  5. Can we determine concavity or inflection points for f(x)f(x)?

Tip: When working with logarithmic functions, always check for domain restrictions, especially ensuring that the argument of the logarithm is positive.

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Math Problem Analysis

Mathematical Concepts

Logarithmic Functions
Derivatives
Domain and Range

Formulas

f(x) = ln(3 - x) + 2
f'(x) = -1 / (3 - x)

Theorems

Derivative of natural logarithmic functions
Domain restrictions for logarithmic functions

Suitable Grade Level

Grades 10-12