Final answer:
To find (f-g)(x) for the functions f(x) = 2x² - 5x + 1 and g(x) = -2x + 4, we subtract g(x) from f(x) which results in the new function 2x² - 3x - 3.
Step-by-step explanation:
To operate (f-g)(x), we need to subtract the function g(x) from the function f(x). We are given f(x) = 2x² - 5x + 1 and g(x) = -2x + 4.
First, we write out the functions:
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- f(x) = 2x² - 5x + 1
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- g(x) = -2x + 4
Now we subtract g(x) from f(x):
(f-g)(x) = (2x² - 5x + 1) - (-2x + 4)
To subtract, we distribute the negative sign across g(x):
(f-g)(x) = 2x² - 5x + 1 + 2x - 4
Combine like terms:
(f-g)(x) = 2x² - 3x - 3
The result of the operation (f-g)(x) is 2x² - 3x - 3.