If f(x)=x(1−x) for any x, then f(1−x) . . .

[VJesus12]

If f(x)=x(1−x) for any x, then f(1−x) must be equal to which of the following?

A. x
B. f(x)
C. f(x−1)
D. x2
E. 1−x

The OA is B.

Can I solve this PS question using particular numbers? What is the best way to get the correct solution?

[MonkeyD.Luffy]

If f(x)=x(1−x) for any x, then f(1−x) must be equal to which of the following?

A. x
B. f(x)
C. f(x−1)
D. x2
E. 1−x

The OA is B.

Can I solve this PS question using particular numbers? What is the best way to get the correct solution?

F(x) itself

[ErikaPrepScholar]

Rather than plugging in numbers, your best move is to plug in 1-x for x in the initial function and see what it equals. Plugging in numbers is a dangerous game, since it might work for certain answers with some numbers, but not with other numbers.

So here, plugging in 1-x for x gives $$f\left(1-x\right)=\left(1-x\right)\left(1-\left(1-x\right)\right)$$ $$f\left(1-x\right)=\left(1-x\right)\left(1-1+x\right)$$
$$f\left(1-x\right)=\left(1-x\right)x$$

At this point we should notice that this is identical to f(x) as given in the question stem. This gives B as the correct answer.

[Brent@GMATPrepNow]

If f(x)=x(1−x) for any x, then f(1−x) must be equal to which of the following?

A. x
B. f(x)
C. f(x−1)
D. x²
E. 1−x

f(x) = x(1−x)
So, for example, if x = 3, then f(3) = 3(1−3) = -6
Likewise, if x = 2k, then f(2k) = (2k)(1−2k) = 2k - 4k²

So, f(1 − x) = (1 − x)(1 − (1−x))
= (1 - x)( x)
= (x)(1 - x)

This is the same as the original function, f(x)

Answer: B

Cheers,
Brent