Question

Let f(x) = 2x-5and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if

• A. 5/2<x<7/2
• B. x≤5/2 or x≥7/2
• C. x<5/2 or x≥7/2
• D. 5/2≤x≤7/2

Answer 1

Answer: (D)

5/2≤x≤7/2

Answer 2

The correct answer is (D):
f(x) = 2x - 5, g(x) = 7 - 2x.
Given, |f(x) + g(x)| = |f(x)| + |g(x)
2 = |f(x)| + |g(x)|
In the 3 ranges (- ∞,5/2), [5/2,7/2] and [7/2,∞),
|f(x)|+|g(x)| = 2 only when x ∈ [5/2,7/2]