Pretest: Unit 3 Question 16 of 20
For R(x) = 4x + 2 and g(x) = x2 - 6, find (f+g)(x).
A. 4x3 - 4
B. x2 + 4x - 4
O c. 4x2 - 16
O D. x2 + 4x+8
BMI

(f + g)(x) = x² + 4x - 4 ⇒ B

Step-by-step explanation:

Let us solve the question

∵ f(x) = 4x + 4

∵ g(x) = x² - 6

→ We need to find (f + g)(x) which means f(x) + g(x)

∴ (f + g)(x) = f(x) + g(x)

∵ f(x) + g(x) = (4x + 2) + (x² - 6)

∴ f(x) + g(x) = 4x + 2 + x² - 6

→ Add the like terms

∵ f(x) + g(x) = 4x + x² + (2 - 6)

∴ f(x) + g(x) = 4x + x² + (-4)

→ Remember (+)(-) = (-)

∴ f(x) + g(x) = 4x + x² - 4

→ Arrange the terms from greatest power of x

∴ f(x) + g(x) = x² + 4x - 4

∴ (f + g)(x) = x² + 4x - 4

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