Answer:
A possible value of x for which g(x) = √(x-1)(x-2) is undefined is x = 1.5
Step-by-step explanation:
The function g(x) = √(x-1)(x-2) is undefined when (x-1)(x-2) < 0.
So (x-1)(x-2) < 0
⇒ x - 1 < 0 or x -2 < 2
⇒ x < 1 or x < 2.
So we look for the interval for which (x - 1)(x - 2) < 0
when x < 1, e.g x = 0, (x - 1)(x - 2) = (0 - 1)(0 - 2) = (-1)(-2) =2 > 0. So (x - 1)(x - 2) > 0 for x < 1
when 1 < x < 2, e.g x = 1.5, (x - 1)(x - 2) = (1.5 - 1)(1.5 - 2) = (0.5)(-0.5) = -0.25 < 0. So (x - 1)(x - 2) < 0 for 1 < x < 2
when x > 2 e.g x = 3, (x - 1)(x - 2) = (3 - 1)(3 - 2) = (2)(1) = 2 > 0. So (x - 1)(x - 2) > 0 for x > 2
Since (x - 1)(x - 2) < 0 for 1 < x < 2, this is the required interval.
So, g(x) = √(x-1)(x-2) is undefined in the interval 1 < x < 2
A possible value for x in this interval is x = 1.5
So, a possible value of x for which g(x) = √(x-1)(x-2) is undefined is x = 1.5
