# Quantitative Aptitude – Algebra – Functions – Let f(x) = 2x-5 and g(x) = 7-2x

## Question

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 ≤ 5/2 or x ≥ 7/2
C) x < 5/2 or x ≥ 7/2
D) 5/2 ≤ x ≤ 7/2

Option (D)

## Solution

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 – 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 ≥ 7/2
2x-5 – 7+2x = 2
x=7/2
So, the answer should be 5/2<= x <= 7/2
Option (D)

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