Function f(x) is defined as follows: If x is… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

Function $f(x)$ is defined as follows: If $x$ is positive or 0, then $f(x) = 1 - x$ ; If $x$ is negative, then $f(x) = x - 1$ . Which of the following statements must be true? I. $f(|x|) = |f(x)|$ II. $f(x) = f(-x)$ III. $|f(x + 1)| = |x|$

Correct answer marked below

I only

II only

III only

Correct

I and III only

None of the above

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Explanation

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Official Explanation

Official

f(|x|) = |f(x)|

. This option is not necessarily true.

Consider

x = -1

f(|x|) = f(1) = 1 - 1 = 0

does not equal

|f(x)| = |f(-1)| = |-1 - 1| = |-2| = 2

.

II.

f(x) = f(-x)

. This option is not necessarily true.

Consider

x = 1

f(x) = f(1) = 1 - 1 = 0

does not equal

f(-x) = f(-1) = -1 - 1 = -2

.…

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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.