https://file.aiquickdraw.com/mathbot/file/1727172655635l3id7gjd.pdf

The document you uploaded contains several math problems, written in Arabic, which include inequalities, composite functions, and questions related to the properties of functions. Below is a brief overview of the problems found:

1. **Inequalities**:
   - Solve a series of inequalities involving linear and absolute value terms.
   
2. **Functions and Composition**:
   - Given two functions \( f(x) = x + 1 \) and \( g(x) = x - 3 \), find:
     - \( f \circ g \) (composition of functions),
     - Domain of \( f \circ g \),
     - Evaluate \( (f \circ g)(3) \).
     
3. **Function properties** (Parabolas and square roots):
   - For \( f(x) = 1 - x^2 \):
     - Find its domain and range.
     - Determine whether it is an even or odd function.
     - Study the monotonicity of the function.
   - For \( f(x) = \sqrt{1 - x^2} \):
     - Find its domain and range.
     - Determine if it is an even or odd function.
     - Study whether the function is bounded.
     
4. **Monotonic functions**:
   - Prove that the function \( f(x) = 2 - 3x \), defined on \( \mathbb{R} \), is monotonic and find its inverse.

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Would you like me to solve any of these problems? If yes, please specify which one.

Here are 5 possible follow-up questions:
1. How do you solve compound inequalities?
2. What is the domain and range of a composite function?
3. How can you determine if a function is even or odd?
4. What does it mean for a function to be bounded?
5. How do you find the inverse of a monotonic function?

**Tip**: In function composition, always substitute one function into the other carefully, considering the domains of both functions to avoid undefined values.

Solve the following math problems: inequalities, function composition, properties of functions, and monotonicity.

This guide covers solving linear inequalities, performing function composition, and understanding function properties like domain, range, evenness, oddness, monotonicity, and boundedness. Learn how to prove monotonicity and find inverse functions. Suitable for Grades 9-12.

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