Question

Domain: x ≠ √2, x ≠ -√2

A. x > 2
B. x < 2
C. x > -2
D. x < -2

Answer 1

The domain x ≠ √2, x ≠ -√2 means that x cannot be equal to the square root of 2 or the negative square root of 2. The options A and B are not valid as they include √2 and -√2, but options C and D are valid as they do not include √2 or -√2.

Step-by-step explanation:

The given domain is x ≠ √2, x ≠ -√2. This means that x cannot be equal to the square root of 2 or the negative square root of 2. To determine the range of values for x, we need to find the numbers that are greater than or less than 2.

1. Since x cannot be equal to √2 or -√2, it can be any real number except the square root of 2 and the negative square root of 2.
2. Therefore, x > 2 is not a valid option as it includes √2 which is not allowed.
3. Similarly, x < 2 is also not a valid option as it includes -√2 which is not allowed.
4. However, x > -2 and x < -2 are valid options as they do not include √2 or -√2.

So, the correct answer is C. x > -2 and D. x < -2.