Question

Which inequality represents all values of x for which the quotient √(6x²)/√4x is defined?

a) x > 0
b) x ≥ 0
c) x > 1/4
d) x ≥ 1/4

Answer 1

The correct inequality is x ≥ 0.

Step-by-step explanation:

To find the inequality that represents all values of x for which the quotient of √(6x²) and √4x is defined, we need to consider the domain of the square roots. Both square roots are defined only when the radicands (what's inside the square root) are non-negative. So we have:

The radicands √(6x²) and √4x must be non-negative:

6x² ≥ 0 and 4x ≥ 0

Solving these inequalities, we get:

x ≥ 0 and x ≥ 0

Since both inequalities have the same solution, we can write it as:

x ≥ 0

Therefore, the correct inequality that represents all values of x for which the given quotient is defined is x ≥ 0.