The required difference in the expression (f – g)(x) is - 6x³+ 4x² + 4x - 8
Given the following functions
f(x) = 2x² + 4x - 5
g(x) = 6x³ – 2x² + 3
In order to get the required function (f-g)(x), we will have to take the difference of the function as shown:
(f – g)(x) = f(x) - g(x)
Substitute the given parameters into the expression
(f – g)(x) = 2x² + 4x - 5 - (6x³ – 2x² + 3)
Expand
(f – g)(x) = 2x² + 4x - 5 - 6x³ + 2x² - 3
Collect the like terms
(f – g)(x) = 2x²+2x²- 6x³ + 4x -5 -3
(f – g)(x) = - 6x³+ 4x² + 4x -5 -3
(f – g)(x) = - 6x³+ 4x² + 4x - 8
Hence the required difference in the expression (f – g)(x) is - 6x³+ 4x² + 4x - 8
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