Question

if (f(x) = |x| + 9) and (g(x) = -6), which describes the range of ((f + g)(x))?

((f + g)(x) ge 3) for all values of (x)
((f + g)(x) le 3) for all values of (x)
((f + g)(x) le 6) for all values of (x)
((f + g)(x) ge 6) for all values of (x)

Explanation:

Find the sum function

$$ (f+g)(x) = f(x) + g(x) = |x| + 9 + (-6) = |x| + 3 $$

Determine the range of the sum function

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Answer:

• (f + g)(x) ≥ 3 for all values of x (Correct answer)
• (f + g)(x) ≤ 3 for all values of x
• (f + g)(x) ≤ 6 for all values of x
• (f + g)(x) ≥ 6 for all values of x