Let f(x) = 2x – 5 and g(x) = 7 – 2x. Then |f(… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

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

Correct answer marked below

\frac{5}{2} < x < \frac{7}{2}

x \leq \frac{5}{2}

x \geq \frac{7}{2}

x < \frac{5}{2}

x \geq 7/2

\frac{5}{2} \leq x \leq \frac{7}{2}

Correct

\frac{5}{2} \leq x

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Explanation

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Official Explanation

Official

We have

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

.

Substitute the functions:

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

.

Simplify:

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

, so

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

.

This equality holds only when both absolute values are non‑negative, i.e., when

2x - 5 \geq 0

and

7 - 2x \geq 0

.…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.