For which of the following functions is $f(a-b)=f(a)f(b)$ for all numbers a and b?

Answer Choices

Correct answer marked below

f(x)=x^3

f(x)=|5x+1|

f(x)=4x^3-x

f(x)=2-3x

f(x)=1

Correct

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Comments

RajeshJun 11

Is this really a 655-705? I got E pretty quickly by just testing a=0, b=0. Maybe I'm missing something about the other choices being tempting if you don't plug in carefully.

SusieAug 16

I initially picked A because x^3 felt right with the exponent-looking structure, but then I realized f(a)f(b) would need (ab)^3, not (a-b)^3. Classic careless mistake on my end.

RanjeetAug 24

This one took me longer than I'd like. I kept trying to prove it algebraically for each choice until I realized you can just eliminate with a=1, b=1 and a=0, b=0. Is that the intended approach or is there a cleaner way?

AdityaSep 6

Respect to whoever designed D, because 2-3x looks so close to something that might work but f(a)f(b) expands to a mess. Nice distractor.

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.

For which of the following functions is f(a−b)=f(a)f(b)f(a-b)=f(a)f(b)f(a−b)=f(a)f(b) for all numbers a and b?