Let's work through the questions visible in your image, which involves the functions $f(x)$ and $g(x)$ displayed as graphs.

Step-by-step approach:

1. For $f(1) + g(2)$:

   • $f(1)$: From the graph of $f(x)$, locate $x = 1$. The corresponding $y$-value appears to be 4.
   • $g(2)$: From the graph of $g(x)$, locate $x = 2$. The corresponding $y$-value appears to be 5.
   • $f(1) + g(2) = 4 + 5 = 9$.

2. For $f(1) \cdot g(5)$:

   • $f(1)$: As calculated before, $f(1) = 4$.
   • $g(5)$: From the graph of $g(x)$, locate $x = 5$. The corresponding $y$-value is 2.
   • $f(1) \cdot g(5) = 4 \cdot 2 = 8$.

3. For $g(5) - f(4)$:

   • $g(5)$: From the graph of $g(x)$, $g(5) = 2$.
   • $f(4)$: From the graph of $f(x)$, locate $x = 4$. The corresponding $y$-value is 3.
   • $g(5) - f(4) = 2 - 3 = -1$.

4. For $\frac{g(2)}{f(4)}$:

   • $g(2)$: From the graph of $g(x)$, $g(2) = 5$ (as previously calculated).
   • $f(4)$: From the graph of $f(x)$, $f(4) = 3$ (as previously calculated).
   • $\frac{g(2)}{f(4)} = \frac{5}{3}$.

Final answers:

• $f(1) + g(2) = 9$
• $f(1) \cdot g(5) = 8$
• $g(5) - f(4) = -1$
• $\frac{g(2)}{f(4)} = \frac{5}{3}$

Would you like further details or clarifications?

Here are five related questions to deepen your understanding:

1. How do you interpret the operations on functions graphically?
2. What happens when the value of $f(x)$ or $g(x)$ is zero?
3. How would the result change if you had $f(x) - g(x)$ instead of $f(x) + g(x)$?
4. What are the practical applications of performing operations like $f(x) \cdot g(x)$?
5. Can function operations like division always be performed, or are there restrictions?

Tip: When multiplying or dividing functions, be cautious of values that make one of the functions zero, as they could impact the solution.