Question

Which inequality represents all values of x for which the quotient below is defined? √15(x-1) ÷ √2^2

Answer 1

Option D: x ≥ 1.

Explanation:

Here we have the quotient:

`(√(15*(x - 1)) )/(√(2*x^2) )`

Here we have two restrictions for the domain.

first, the denominator can never be zero, so x must be different than zero.

Second, the arguments of the square roots can not be negative.

The one in the denominator is always positive because we have the square of x.

So let's look at the values of x, such that:

15*(x - 1) ≥ 0

(x - 1) ≥ 0

x ≥ 1

Note that when x ≥ 1, we are also removing the problem in the denominator, then we can conclude that the fraction is defined when:

x ≥ 1.

The correct option is D