Let me analyze the image and solve the problems presented in the assignment step by step. The tasks involve finding compositions of functions, domains, ranges, and evaluating functions. I'll start solving some parts; let me know where you'd like to focus!

Key Information in the Problem:

1. Tasks for #13–16:
   • Find $f \circ g(x)$ and $g \circ f(x)$, and state their domain and range.
2. Tasks for #21–35:
   • Evaluate composite functions using $f(x) = 3x$, $g(x) = x + 4$, and $h(x) = x^2 - 1$.

Examples of Solutions:

Problem 13:

• $f(x) = 2x$, $g(x) = x + 5$
  1. $f \circ g(x) = f(g(x)) = f(x + 5) = 2(x + 5) = 2x + 10$
     Domain: All real numbers ($\mathbb{R}$)
     Range: All real numbers ($\mathbb{R}$)
  2. $g \circ f(x) = g(f(x)) = g(2x) = 2x + 5$
     Domain: $\mathbb{R}$
     Range: $\mathbb{R}$

Problem 21:

Evaluate $f(g(1))$:

• Step 1: $g(1) = 1 + 4 = 5$
• Step 2: $f(5) = 3(5) = 15$
  Answer: $f(g(1)) = 15$

Problem 22:

Evaluate $g(h(0))$:

• Step 1: $h(0) = 0^2 - 1 = -1$
• Step 2: $g(-1) = -1 + 4 = 3$
  Answer: $g(h(0)) = 3$

Would you like detailed solutions for specific problems, domains, or ranges? Here are questions and tips to guide you:

1. Do you need help with #14–16 or just the composition for #13–16?
2. Shall I explain how to find the domains and ranges for compositions?
3. Should we evaluate more composite values (#23–35)?
4. Are you familiar with the order of composition $f \circ g(x)$ vs $g \circ f(x)$?
5. Would you like an explanation for step-by-step substitutions?

Tip: When evaluating $f \circ g$, remember the output of $g(x)$ becomes the input for $f(x)$.