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

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.