Question

For f(x)=4x+1 and g(x)=x2-5, find (f-g)(x)

Answer 1

(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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