To determine which option is the largest when x lies between 0 and 1, let's analyze each option:
A) x: This option represents the value of x itself. Since x lies between 0 and 1, the value of x will always be less than or equal to 1. Therefore, option A is not the largest.
B) x^2: This option represents the square of x. When x lies between 0 and 1, squaring x will always result in a smaller value. For example, if x = 0.5, x^2 = 0.25. Therefore, option B is not the largest.
C) -x: This option represents the negative value of x. Since x lies between 0 and 1, the negative value of x will always be negative and less than 0. Therefore, option C is not the largest.
D) 1/x: This option represents the reciprocal of x. When x lies between 0 and 1, the reciprocal of x will always be greater than 1. For example, if x = 0.5, 1/x = 1/0.5 = 2. Therefore, option D is the largest.
Hence, the correct answer is option D) 1/x. This option is the largest when x lies between 0 and 1 because it represents the reciprocal of x, which is always greater than 1.