Let f(x) = 2x-5 and 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 â‰¤ 5/2 or x â‰¥ 7/2

C) x < 5/2 or x â‰¥ 7/2

D) 5/2 â‰¤ x â‰¤ 7/2

Option (D)

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,

|f(x) + g(x)| = |f(x)| + |g(x)|

Putting value of f(x) and g(x), we get,

|2x-5| + |7-2x| = 2

1st Case: When x<=5/2

-2x + 5 +7 â€“ 2x = 2

=> x=5/2

2nd Case: 5/2 < x < 7/2

On solving, we get, 2=2, which satisfies the condition

3rd Case: x â‰¥ 7/2

2x-5 â€“ 7+2x = 2

x=7/2

So, the answer should be 5/2<= x <= 7/2

Option (D)

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