CAT 2017 Slot 2 — QA Question 32

Now

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

This is true only if both f(x) and g(x) are both negative or both positive or both are zero

Case 1: Now if both f(x) and g(x) are greater than or equal to zero.

f(x) = 2x - 5 ≥ 0 or x ≥ $\frac{5}{2}$

g(x) = 7 - 2x ≥ 0 or x ≤ $\frac{7}{2}$

∴$\frac{5}{2}\le x\le \frac{7}{2}$

Case 2: Now if both f(x) and g(x) are less than or equal to zero.

f(x) = 2x - 5 ≤ 0 or x ≤ $\frac{5}{2}$

g(x) = 7 - 2x ≤ 0 or x ≥ $\frac{7}{2}$

This means x ≥ $\frac{7}{2}$ and x ≤ $\frac{5}{2}$.

However, this is not possible.

Hence, option (d).