Let f(x) = \min\x^2 - 2, 1 - 2x\, for any pos… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

Let $f(x) = \min\{x^2 - 2, 1 - 2x\}$ , for any positive number $x$ . What is the maximum value of $f(x)$ ?

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-1

Correct

-2

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Explanation

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Official Explanation

Official

Breaking Down the Info: This function finds the minimum between two values. The left value increases with x, while the right value decreases with x.

If we want the maximum value of this function, we should find the equilibrium point.

Set

x^2 - 2 = 1 - 2x

, which gives

x^2 + 2x - 3 = 0

.

Factor:

(x + 3)(x - 1) = 0

, so

x = -3

x = 1

.

We are not allowed to take negative x (since x is positive), so we consider

x = 1

.…

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What this question tests

What it tests

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

Common trap

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

Let f(x)=min⁡{x2−2,1−2x}f(x) = \min\{x^2 - 2, 1 - 2x\}f(x)=min{x2−2,1−2x}, for any positive number xxx. What is the maximum value of f(x)f(x)f(x)?