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just pick number x=-4 and compute...
sqrt(-x|x|) = sqrt(16) = 4
now check the answer choices...
it is certainly not 1 or -1, it is not x (which is -4 and the answer is 4) and certainly not sqrt(x) which is undefined.
it is, however exactly -x. so the answer is A
also, if you are attentive enough to details, you should notice that
sqrt(something) is always positive, and x is negative (given in the stem) hence answer cannot be x (neither can it be -1 for the same reason).