Given the functions:

• $f(x) = 5x + 7$
• $g(x) = 3x - 5$

We need to find $(f - g)(x)$.

Step 1: Subtract $g(x)$ from $f(x)$

$(f - g)(x) = f(x) - g(x)$

Substituting the given functions:

$(f - g)(x) = (5x + 7) - (3x - 5)$

Step 2: Simplify the expression

$(f - g)(x) = 5x + 7 - 3x + 5$ $(f - g)(x) = (5x - 3x) + (7 + 5)$ $(f - g)(x) = 2x + 12$

Final answer:

$(f - g)(x) = 2x + 12$

Domain:

Both $f(x)$ and $g(x)$ are linear functions, and the subtraction of two linear functions is also linear. Therefore, the domain is all real numbers: $\text{Domain of } (f - g)(x): \ (-\infty, \infty)$

Would you like details on any step, or have any questions?

Here are 5 related questions:

1. What is $(f + g)(x)$ for the same functions?
2. How do you find the domain of a function with a square root?
3. What is the product of $f(x)$ and $g(x)$?
4. What is the composition $f(g(x))$?
5. How do you find the inverse of a function?

Tip: Always simplify step-by-step, especially when dealing with multiple terms!