Consider the function defined as g(x) = | 1x – 4| – x. What is the value of g( 13) =

Consider the function defined as g(x) = | 1x… | GMAT Sprint

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sub-505

Absolute Values/Modules

Consider the function defined as $g(x) = |\frac{1}{x} – 4| – x$ . What is the value of $g(\frac{1}{3}) =$

Answer Choices

Correct answer marked below

–2/3

–1/3

1/3

2/3

Correct

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Explanation

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Official Explanation

Official

To find

g(\frac{1}{3})

, we start with the function

g(x) = |\frac{1}{x} – 4| – x

. Thus,

g(\frac{1}{3}) = |\frac{1}{(1/3)} – 4| – \frac{1}{3}

. This…

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Comments

YashFeb 1, 2024

Tricky wording but good practice

2020MEB098Mar 8, 2025

thanks for taking time to upload it!

What this question tests

What it tests

Your ability to solve absolute-value equations and inequalities by considering both cases.

Common trap

Dropping the absolute value bars entirely or missing that |x| = k has two solutions when k > 0.

Consider the function defined as g(x)=∣1x–4∣–xg(x) = |\frac{1}{x} – 4| – xg(x)=∣x1​–4∣–x. What is the value of g(13)=g(\frac{1}{3}) =g(31​)=