Question

which inequality represents all values of x for which the quotient below is defined?

$\sqrt{7x^2 divided by \sqrt{3x} \\A. x \ \textgreater \ 1 \\B. x \ \textgreater \ -1\\C. x \ \textgreater \ 0\\D. x \geq 0$

Answer 1

Answer:

C. x>0

Step-by-step explanation:

The given quotient is

$\frac{ \sqrt{7 {x}^{2} } }{ \sqrt{3x} }$

Recall that the expression in the denominator should not be equal to zero.

Also the expression under the radical should be greater than or equal to zero.

This means that we should have:

$\frac{7 {x}^{2} }{3x} \: > \: 0$

This implies that:

$x \: > \: 0$

Option C is correct