Final answer:
To find (f-g)(x) for the functions f(x)=3x²-2x and g(x)=1-4x², subtract g(x) from f(x) and combine like terms to get the simplified result: 5x² - 2x - 1. Option C is correct.
Step-by-step explanation:
To find and simplify (f-g)(x) where f(x)=3x²-2x, and g(x)=1-4x², you subtract the function g(x) from the function f(x).
Here is the step-by-step calculation:
Write out the functions being subtracted: (f-g)(x) = f(x) - g(x).
Substitute the given functions into the equation: (f-g)(x) = (3x² - 2x) - (1 - 4x²).
Distribute the negative sign through the second function: (f-g)(x) = 3x² - 2x - 1 + 4x².
Combine like terms: (f-g)(x) = 5x² - 2x - 1.
The simplified form of (f-g)(x) is 5x² - 2x - 1.
To find (f−g)(x), we need to subtract g(x) from f(x).
So, (f−g)(x) = f(x) - g(x).
Given f(x) = 3x²−2x and g(x) = 1−4x²:
(f−g)(x) = (3x²−2x) - (1−4x²)
Expanding this expression, we get: (f−g)(x) = 3x²−2x - 1+4x²
Combining like terms, we simplify further to get: (f−g)(x) = (3x² + 4x²) - (2x + 1)
Finally, (f−g)(x) = 5x² - 2x - 1.