Question

Which inequality represents all values of x for which the quotient below is defined? √(8x²) / (√(2x))

a) x ≠ 0
b) x > 0
c) x ≥ 0
d) x < 0

Answer 1

The inequality that represents all values of x for which √(8x²) / (√(2x)) is defined is b) x > 0, since the denominator must be greater than zero.

Step-by-step explanation:

The question revolves around finding the domain of the function √(8x²) / (√(2x)). For the quotient to be defined, the denominator √(2x) cannot be zero, and it must be a real number. Thus, the value of x must be such that 2x > 0 which simplifies to x > 0 since the square root of a negative number is not defined in the real number system. The correct answer to this inequality that represents all values of x for which the quotient is defined is x > 0 which is option b) x > 0.