Given the functions f(x) = |x - 3| and g(x) =… | GMAT Sprint

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PS · Problem Solving

605-655

Absolute Values/Modules

Given the functions $f(x) = |x - 3|$ and $g(x) = |x + 1|$ , what is the range of all possible values of x for which $f(g(x)) = 0$ ?

Answer Choices

Correct answer marked below

-6

-4

Correct

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Explanation

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Official Explanation

Official

To solve for the values of x such that

f(g(x)) = 0

, we first need to determine when

f(x) = 0

. The function

f(x) = |x - 3|

equals zero when its argument is zero, which occurs at

x = 3

. Therefore, we need

g(x) = 3

. The function

g(x) = |x + 1|

equals 3 when

x + 1 = 3

x + 1 = -3

. Solving these equations gives us

x = 2

and

x = -4

. Thus, the values of x that satisfy

f(g(x)) = 0

are

x = -4

and

x = 2

.…

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Comments

JayaJan 2, 2025

Thank for sharing!

AdityaFeb 1, 2025

got this wrong on my practice

SoumyaAug 10, 2024

thankss

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.

Given the functions f(x)=∣x−3∣f(x) = |x - 3|f(x)=∣x−3∣ and g(x)=∣x+1∣g(x) = |x + 1|g(x)=∣x+1∣, what is the range of all possible values of x for which f(g(x))=0f(g(x)) = 0f(g(x))=0?