Question 38

For 1

Within the interval 1

A) 3-2x

This option is incorrect because, within the specified interval, the expression |x - 1| + |x - 2| does not simplify to 3 - 2x. In fact, substituting values from the interval into 3 - 2x does not yield a constant output of 1.

B) 2x-3

This option is also incorrect. The expression |x - 1| + |x - 2| does not simplify to 2x - 3 for x values between 1 and 2. Instead, this expression yields a variable result that is not constant like the correct answer.

C) 2x + 3

This option is incorrect because it does not reflect the behavior of the expression |x - 1| + |x - 2| in the given interval. The output of 2x + 3 increases with x and does not equate to the constant value of 1.

D) 1

This option is correct. For all x values in the range from 1 to 2, the expression |x - 1| + |x - 2| consistently evaluates to 1. For example, at x = 1, it equals 1; at x = 2, it also equals 1.

Conclusion

The correct answer is 1 because it accurately represents the result of the expression |x - 1| + |x - 2| for all x within the interval 1 to 2. Other options fail to provide a constant value and do not align with the behavior of the absolute value expression in the specified range.