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We are tasked with finding \( (f - g)(x) \), given that:

- \( f(x) = 5x + 3 \)
- \( g(x) = 2x - 1 \)

To find \( (f - g)(x) \), we subtract the functions:

\[
(f - g)(x) = f(x) - g(x)
\]

Substituting the given functions:

\[
(f - g)(x) = (5x + 3) - (2x - 1)
\]

Simplify the expression:

\[
(f - g)(x) = 5x + 3 - 2x + 1
\]
\[
(f - g)(x) = (5x - 2x) + (3 + 1)
\]
\[
(f - g)(x) = 3x + 4
\]

Thus, the correct option is **a) \( 3x + 4 \)**.

Would you like more details or have any further questions? Here are some related questions:

1. How do we add or subtract two functions?
2. Can you explain the process of combining like terms in algebraic expressions?
3. How would the result change if \( f(x) \) or \( g(x) \) had different coefficients?
4. How do we apply the same method for multiplying two functions \( f(x) \cdot g(x) \)?
5. What happens if you subtract functions with non-linear terms?

**Tip:** Always carefully distribute the negative sign when subtracting functions or expressions.

Escoja la opción correcta: (f - g)(x) es igual a _______ si: f(x)= 5x + 3 y g(x)= 2x - 1

Learn how to subtract two functions, f(x) = 5x + 3 and g(x) = 2x - 1, to find (f - g)(x). This algebraic problem focuses on function operations and is suitable for students in Grades 7-9.

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