The domain of y=the square root of bx to the power of two -2 is undefined, which of the following best describes the value of 'b'?
a)b is less than or equal to 0
b)b<0
c)b=0
d)b is greater than or equal to 0
I can't quite parse your language. Do you mean
y = √(bx)^-2
or some other arrangement?
If that is what you meant, then b=0 will make the domain an empty set.
all good the bx but to the power of 2, not -2 then minus 2.
To determine the domain of the function y = √(bx^2 - 2), we need to check for any values of 'b' that would make the expression under the square root negative, resulting in an undefined value for y.
For the square root function, the expression under the square root (√) must be greater than or equal to 0.
Thus, we need to find the values of 'b' such that bx^2 - 2 ≥ 0.
Now, since bx^2 - 2 ≥ 0, we can solve this inequality for 'b'.
Adding 2 to both sides, we have bx^2 ≥ 2.
Dividing both sides by x^2 (assuming x^2 ≠ 0), we get b ≥ 2 / x^2.
The expression 2 / x^2 will always be positive or zero for any non-zero value of x.
Therefore, to ensure that bx^2 - 2 is positive or zero, b must be either greater than or equal to 0.
Hence, the correct answer is:
d) b is greater than or equal to 0