Which of the following expressions, if any, are equal for all real numbers x

Which of the following expressions, if any, are equal for all real numbers x ?

  1. √(-x)2
  2. ⎪-x⎪
  3. -⎪x⎪
  1. I and II only
  2. I and III only
  3. II and III only
  4. I, II, and III
  5. None of the expressions are equivalent

Answer

The correct answer is A.

I. If x is a negative number or positive number, its square will always be positive. The value will be equal to x.

II. Here also, the value will be x as modulus of positive or negative number is always positive.

III. In this case, the result will be negative.