Question

which inequality represents all values of x for which the quotient below is defined?
`√(x + 1) / √(3 - x)`a.
`- 1 \leqslant x \leqslant 3`b.
`x \leqslant 3`c.
`- 1 \leqslant x \ \textless \ 3`d.
`x \geqslant - 1`

Answer 1

C. -1 ≤ x < 3

Step-by-step explanation:

The quotient is defined when the values inside the square root are positive and when the divisor is different from zero.

Then, the value in the square root of the dividend is positive when:

x + 1 ≥ 0

So, solving for x, we get:

x + 1 - 1 ≥ 0 - 1

x ≥ -1

Additionally, the value in the square root of the divisor is positive and different from zero when:

3 - x > 0

So, solving for x, we get:

3 - x + x > 0

3 > x

or

x < 3

Therefore, the solution is the set of all x that are greater or equal to -1 but are less than 3. So, the answer is:

-1 ≤ x < 3