Final answer:
To find (f - g)(x), you subtract g(x) from f(x). For f(x) = x^2 + 4x and g(x) = 2 - x, (f - g)(x) is calculated as x^2 + 5x - 2.
Step-by-step explanation:
To find (f - g)(x), we must subtract the function g(x) from f(x). The given functions are f(x) = x^2 + 4x and g(x) = 2 - x. Here's the step-by-step process:
- Write down the functions: f(x) = x^2 + 4x, g(x) = 2 - x.
- Subtract g(x) from f(x): (f - g)(x) = (x^2 + 4x) - (2 - x).
- Distribute the negative sign across the terms in g(x): (f - g)(x) = x^2 + 4x - 2 + x.
- Combine like terms: (f - g)(x) = x^2 + 5x - 2.
First, let's find the expression for f(x) - g(x):
f(x) - g(x) = (x^2 + 4x) - (2 - x).
Next, simplify the expression:
f(x) - g(x) = x^2 + 4x - 2 + x.
Finally, combine like terms to get the final answer:
f(x) - g(x) = x^2 + 5x - 2.
The result of (f - g)(x) is x^2 + 5x - 2.