Question

Which of the following inequalities represents all values of X for which the quotient below is defined?

Answer 1

Answer:

$x \ge 1$

Step-by-step explanation:

Given

$\sqrt{6(x - 1)} \div \sqrt{3x^2$

Required

x for $which$ the function is $de fi ned$

To do this, we set the numerator root $\ge 0$

So, we have:

$6(x - 1) \ge 0$

Divide by 6

$(x - 1) \ge 0$

Solve for x

$x \ge 1$

Also, we set the denominator greater than 0:

$3x^2 > 0$

Divide by 3

$x^2 > 0$

Take square roots

$x > 0$

So, we have:

$x > 0$ and $x \ge 1$

Combine both to give:

$x \ge 1$