Let's solve the given questions step by step.

We have two functions:

• $f(x) = 2x + 3$
• $g(x) = 9x - 2$

(a) Find $(f + g)(x)$

$(f + g)(x) = f(x) + g(x) = (2x + 3) + (9x - 2)$ Simplifying: $(f + g)(x) = 2x + 9x + 3 - 2 = 11x + 1$

Now, we are asked to find the domain of $f + g$. Since both $f(x)$ and $g(x)$ are linear functions, which are defined for all real numbers, the domain of $f + g$ is all real numbers: $\text{Domain of } f + g: \ (-\infty, \infty)$ So, the correct choice is B: The domain is {x | x is any real number}.

(b) Find $(f - g)(x)$

$(f - g)(x) = f(x) - g(x) = (2x + 3) - (9x - 2)$ Simplifying: $(f - g)(x) = 2x - 9x + 3 + 2 = -7x + 5$

Similarly, the domain of $f - g$ is also all real numbers since both $f(x)$ and $g(x)$ are linear functions: $\text{Domain of } f - g: \ (-\infty, \infty)$ So, again the correct choice is B: The domain is {x | x is any real number}.

Would you like any further details or clarification on this?

Here are 5 additional related questions to explore:

1. What is the sum of $f(x)$ and $g(x)$ evaluated at $x = 2$?
2. What is the difference between $f(x)$ and $g(x)$ when $x = -1$?
3. What would be the domain of $f(x) \cdot g(x)$?
4. What is the domain of $\frac{f(x)}{g(x)}$?
5. How would you find the composite function $f(g(x))$?

Tip: When dealing with linear functions, the domain is typically all real numbers unless there's division by zero or square roots of negative numbers involved.