Answer: The function is defined in the interval [-4,0)
Step-by-step explanation:
Here the given expression is,
[tex]f(x)=\frac{\sqrt{x+4} }{\sqrt{1-x} }[/tex]
⇒[tex]f(x)=\sqrt{\frac{x+4}{1-x}[/tex]
Since, the function can not be defined if the value inside the square root is negative,
Thus, we can write,
[tex]\frac{x+4 }{1-x} \geq 0[/tex]
⇒ [tex]x+4 \geq 0[/tex]
⇒ [tex]x\geq -4[/tex]
Also, [tex]1-x \geq 0[/tex]
But, if the denominator is zero the function can not be defined.
Thus, [tex]1 - x > 0[/tex]
⇒ 1 > x
Thus, For the function f(x), -4 ≤ x <1
Hence, the Domain of the given function is [-4,0)
