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 g(k) and then substitute it into f(x). We start with the equation

f(g(k)) = 11

. First, we find

g(k) = 4 - k

. Next, we substitute

g(k)

into

f(x)

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

. We set this equal to 11:

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

.…

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Comments

RaymondMar 1, 2025

Thankss

AnshulApr 29, 2025

good question

ApoorvMar 2, 2025

Great question!

BenMar 13, 2025

Great question!

NominFeb 19, 2024

thanks a lot

PrachiFeb 9, 2024

Amazing

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?