To solve \((2f - g)(x)\), we need to compute \(2f(x) - g(x)\).

1. First, find \(f(x)\) and \(g(x)\):
   - \(f(x) = x^2 - 5x\)
   - \(g(x) = 4x + 1\)

2. Now compute \(2f(x)\):
   \[
   2f(x) = 2(x^2 - 5x) = 2x^2 - 10x
   \]

3. Subtract \(g(x)\) from \(2f(x)\):
   \[
   (2f - g)(x) = (2x^2 - 10x) - (4x + 1)
   \]
   Simplify the expression:
   \[
   (2f - g)(x) = 2x^2 - 10x - 4x - 1 = 2x^2 - 14x - 1
   \]

Thus, \((2f - g)(x) = 2x^2 - 14x - 1\).

Would you like further details or clarifications?

Here are 5 related questions you might explore:
1. What happens if we calculate \((f + g)(x)\)?
2. Can we find \((f \cdot g)(x)\) for the same functions?
3. How do we interpret the result of \((2f - g)(x)\) graphically?
4. What is the value of \((2f - g)(x)\) when \(x = 3\)?
5. Can you solve for the roots of \((2f - g)(x) = 0\)?

**Tip:** Always double-check your distribution when multiplying or subtracting functions to avoid simple mistakes.

Discover how to solve function operations like (2f - g)(x) using quadratic and linear functions. Follow a detailed step-by-step solution to understand function subtraction and simplification, suitable for students in Grades 9-10.

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