Question

For what values of x is the expression below defined? radical x plus 4 divided by radical 1 minus x

Answer 1

-4 < = x < 1

Explanation:

hope this helps

Answer 2

Answer: The function is defined in the interval [-4,0)

Explanation:

Here the given expression is,

`f(x)=(√(x+4) )/(√(1-x) )`

⇒
`f(x)=\sqrt{(x+4)/(1-x)`

Since, the function can not be defined if the value inside the square root is negative,

Thus, we can write,

`(x+4 )/(1-x) \geq 0`

⇒
`x+4 \geq 0`

⇒
`x\geq -4`

Also,
`1-x \geq 0`

But, if the denominator is zero the function can not be defined.

Thus,
`1 - x > 0`

⇒ 1 > x

Thus, For the function f(x), -4 ≤ x <1

Hence, the Domain of the given function is [-4,0)