The functions f(x) and g(x) are defined by f(… | GMAT Sprint

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PS · Problem Solving

555-605

Algebra

The functions $f(x)$ and $g(x)$ are defined by $f(x) = 2x^2 + 3$ and $g(x) = 4 - x$ . Given that $f(g(k)) = 11$ , which of the following could be the value of k?

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Correct

3/2

1/4

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Explanation

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Official Explanation

Official

To solve for k, we first need to find the expression for

f(g(k))

. We start by substituting

g(k)

into

f(x)

. First, we find

g(k) = 4 - k

. Now we substitute this into

f(x)

f(g(k)) = f(4 - k) = 2(4 - k)^2 + 3

.

Next, we need to set this equal to 11:

2(4 - k)^2 + 3 = 11

.

Subtract 3 from both sides:

2(4 - k)^2 = 8

.

Now divide both sides by 2:…

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Comments

KartikJan 31, 2025

Great question!

BraedonJan 27, 2025

greatt question!

AmanJan 7, 2025

got this wrong on my practice

KnightSep 17, 2024

thanks!

anjaliJul 13, 2024

good question

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

The functions f(x)f(x)f(x) and g(x)g(x)g(x) are defined by f(x)=2x2+3f(x) = 2x^2 + 3f(x)=2x2+3 and g(x)=4−xg(x) = 4 - xg(x)=4−x. Given that f(g(k))=11f(g(k)) = 11f(g(k))=11, which of the following could be the value of k?