Answer:
The possible values for the variable in the expression are -1, 1, -2, 0, -3, 2, -1, 0, 1.
All the options (a, b, c, d) are true.
Explanation:
To find the possible values for the variable in the expression 3 - 2x √(1 - x), we need to consider the restrictions on the domain of the square root function (√).
For the expression 3 - 2x √(1 - x) to be defined, the expression inside the square root (√(1 - x)) must be greater than or equal to zero.
This is because the square root of a negative number is not a real number.
So, let's solve the inequality 1 - x ≥ 0:
1 - x ≥ 0
x ≤ 1
This means that x can take any value less than or equal to 1.
Therefore, the possible values for the variable in the expression are:
a. -1, 1 (since both -1 and 1 are less than or equal to 1)
b. -2, 0 (since both -2 and 0 are less than or equal to 1)
c. -3, 2 (since both -3 and 2 are less than or equal to 1)
d. -1, 0, 1 (since all three values are less than or equal to 1)
Therefore,
All the options (a, b, c, d) have the correct possible values for the variable in the expression.