(f - g)(x) = - x² + 4x + 6
Step-by-step explanation:
If f(x) and g(x) are two functions, then
- (f + g)(x) = f(x) + g(x)
- (f - g)(x) = f(x) - g(x)
- (f . g)(x) = f(x) . g(x)
- (f/g)(x) = f(x)/g(x), where g(x) ≠ 0
Now lets solve the question
∵ f(x) = 4x + 1
∵ g(x) = x² - 5
- To find (f - g)(x) subtract g(x) from f(x)
∵ (f - g)(x) = f(x) - g(x)
∴ (f - g)(x) = (4x + 1) - (x² - 5)
- Multiply the bracket (x² - 5) by (-) and remember (-)(-) = (+)
∴ (f - g)(x) = 4x + 1 - x² + 5
- Add the like terms in the right hand side
∴ (f - g)(x) = 4x + (1 + 5) - x²
∴ (f - g)(x) = 4x + 6 - x²
- Arrange the terms from the greatest power of x
∴ (f - g)(x) = - x² + 4x + 6
(f - g)(x) = - x² + 4x + 6
Learn more:
You can learn more about the functions in brainly.com/question/9801816
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