The document contains various mathematical problems related to inequalities, composite functions, function properties (like domain, range, even/odd), and transformations. Here is a summary of the main tasks found in the file:

1. Solving Inequalities: A series of inequalities need to be solved for their solution sets. For example, the inequalities listed include expressions like: $2x + 1 \leq 5 \quad \text{and} \quad 3x - 4 > 2$

2. Composite Functions: Given $f(x) = x + 1$ and $g(x) = 2x - 3$, you need to:

   • Find $f \circ g$ (composite function),
   • Determine the domain of $f \circ g$,
   • Compute $(f \circ g)(3)$.

3. Properties of Specific Functions:

   • For $f(x) = 1 - x^2$, find:

     • The domain and range,
     • Determine whether the function is even, odd, or neither,
     • Investigate the monotonicity of the function.

   • For $f(x) = \sqrt{1 - x^2}$, similar properties are required:

     • Domain and range,
     • Even or odd behavior,
     • Check if the function is bounded.

4. Proof of Injectivity and Inverses: You are asked to prove that a function $f(x) = 2 - 3x$ is injective (one-to-one) and then find its inverse.

Let me know which specific problem you'd like to dive into, or if you'd like detailed solutions for all of them!

Follow-up Questions:

1. How do we solve the inequality $2x + 1 \leq 5$?
2. What is the domain of the function $g(x) = 2x - 3$?
3. How can we prove that a function is injective?
4. What are the properties of even and odd functions?
5. How do we find the inverse of $f(x) = 2 - 3x$?

Tip: Always check the domain restrictions when dealing with composite functions, as the range of the inner function must fit within the domain of the outer function.