Question

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

Answer 1

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

Step-by-step explanation:

Here the given expression is,

$f(x)=\frac{\sqrt{x+4} }{\sqrt{1-x} }$

⇒$f(x)=\sqrt{\frac{x+4}{1-x}$

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

Thus, we can write,

$\frac{x+4 }{1-x} \geq 0$

⇒ $x+4 \geq 0$

⇒ $x\geq -4$

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)