Question:
Let f(x) = 2x-5and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Let f(x) = 2x-5and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Updated On: Sep 26, 2024
- 5/2<x<7/2
- x≤5/2 or x≥7/2
- x<5/2 or x≥7/2
- 5/2≤x≤7/2
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The Correct Option is D
Solution and Explanation
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]
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