When f(x)= x^6+1x^3, which of the following is equal to f\left(- 1x\right)?

Free Practice Question

PS · Problem Solving

605-655

Functions

When $f(x)=\frac{x^6+1}{x^3}$ , which of the following is equal to $f\left(-\frac{1}{x}\right)$ ?

Answer Choices

Correct answer marked below

f(x)

-f(x)

Correct

\frac{1}{f(x)}

1-f(x)

(f(x))^3

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Unlock the full explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Create free account Sign in

Comments

DanielApr 19

Got f(-1/x) = -f(x) pretty quickly by just plugging in. But I always second-guess myself when odd powers are involved — is there a faster way than full simplification?

RadhikaApr 20

Honestly plugging in is the fastest here. Just make sure you cube the whole fraction correctly, that's where people slip.

TanujJul 2

Wait, I plugged in and got the negative of the original. Can someone confirm that the x^3 in the denominator is the only thing that flips sign?

AadishJul 3

Yeah, x^6 is even so it stays positive, only the x^3 term changes sign. That's the whole trick.

DonJul 7

This is what got me too. Took me a second to realize (-1/x)^6 = 1/x^6, not negative.

JivagoMay 9

Decent question, took me about 90 seconds. The algebra is clean once you see the even/odd exponent pattern.

RaihanaJun 30

I like how this tests whether you actually understand exponent parity rather than just memorizing function transformations. Solid 600-level question.

What this question tests

What it tests

Your ability to evaluate and compose functions, including unusual defined operations.

Common trap

Applying function operations in the wrong order or ignoring domain restrictions.

When f(x)=x6+1x3f(x)=\frac{x^6+1}{x^3}f(x)=x3x6+1​, which of the following is equal to f(−1x)f\left(-\frac{1}{x}\right)f(−x1​)?