The image contains a series of mathematical function problems under the section "Uji Pemahaman" (Understanding Test), where the task is to determine the formulas for $f + g$, $f - g$, $f \cdot g$, and $\frac{f}{g}$, as well as to determine the domain of the new functions formed.

Here is a breakdown of the first few problems:

Problem 1:

• $f(x) = 2x + 3$
• $g(x) = x^2$

Solutions:

1. $f(x) + g(x) = (2x + 3) + x^2 = x^2 + 2x + 3$
2. $f(x) - g(x) = (2x + 3) - x^2 = -x^2 + 2x + 3$
3. $f(x) \cdot g(x) = (2x + 3) \cdot x^2 = 2x^3 + 3x^2$
4. $\frac{f(x)}{g(x)} = \frac{2x + 3}{x^2}$

Domain:

• For addition, subtraction, and multiplication: All real numbers ($\mathbb{R}$).
• For division: $x \neq 0$, as $g(x) = x^2$ cannot be zero.

Problem 2:

• $f(x) = \sqrt{x}$
• $g(x) = x^2 - 1$

Solutions:

1. $f(x) + g(x) = \sqrt{x} + (x^2 - 1)$
2. $f(x) - g(x) = \sqrt{x} - (x^2 - 1)$
3. $f(x) \cdot g(x) = \sqrt{x} \cdot (x^2 - 1) = \sqrt{x}(x^2 - 1)$
4. $\frac{f(x)}{g(x)} = \frac{\sqrt{x}}{x^2 - 1}$

Domain:

• $f(x) = \sqrt{x}$ requires $x \geq 0$.
• $g(x) = x^2 - 1$ cannot be zero, so $x \neq \pm 1$.

Therefore, the domain for all expressions is $x \geq 0$ and $x \neq \pm 1$.

Would you like me to proceed with more problems or details for this? Feel free to ask any specific questions!

Here are 5 related questions to expand on these problems:

1. How do you determine the domain of a function involving a square root?
2. What happens to the domain when a function involves division by another function?
3. How does multiplying two functions affect their domains?
4. Can you explain how to simplify expressions involving square roots?
5. What is the domain of a polynomial function like $g(x) = x^2$?

Tip: When working with square roots, always ensure the argument inside the square root is non-negative.