Free Practice Question

PS · Problem Solving

705-805

Functions

If $f(x) = -g(-x)$ for all real numbers $x$ , what is the value of $g(f(4))$ , given that $(-4, 7)$ is a point on the graph of $g$ ?

Answer Choices

Correct answer marked below

A

f(7)

-f(7)

Correct

C

f(-7)

D

-f(-7)

E

f(f(7))

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Explanation

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Official Explanation

Official

Since

(-4, 7)

is a point on the graph of

g

, we have

g(-4) = 7

.

Now,

g(f(4)) = g(-g(-4))

because

f(4) = -g(-4)

from the given

f(x) = -g(-x)

.…

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If $f(x) = -g(-x)$ for all real numbers $x$ , what is the value of $g(f(4))$ , given that $(-4, 7)$ is a point on the graph of $g$ ?

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Official Explanation

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What it tests

Common trap

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If f(x)=−g(−x)f(x) = -g(-x)f(x)=−g(−x) for all real numbers xxx, what is the value of g(f(4))g(f(4))g(f(4)), given that (−4,7)(-4, 7)(−4,7) is a point on the graph of ggg?

Answer Choices

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Official Explanation

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What it tests

Common trap

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If $f(x) = -g(-x)$ for all real numbers $x$ , what is the value of $g(f(4))$ , given that $(-4, 7)$ is a point on the graph of $g$ ?