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.