Answer:
option D
Step-by-step explanation:
So we know that [tex]\sqrt{a} \sqrt{b} = \sqrt{ab}[/tex]
Applying this to our function, we have that:
[tex]\sqrt{(x-5)} \sqrt{(x+2)} = \sqrt{(x+2)(x-5)}[/tex]
We know that the argument of a square root should always BE POSITIVE.
So we need to evaluate in which points the expression (x+2)(x-5) is positive.
So we know that (x+2) is possitive when x>-2 and negative when x<-2.
Also we know that (x-5) is possitive when x>5, if x<5 then x is negative.
Then we have:
if x<-2, then:
(x-5) is negative
(x+2) is negative
Then (x+2)(x-5) is positive.
If x>5 then:
(x-5) is positive
(x+2) is positive.
Then (x+2)(x-5) is positive.
If -2<x<5 then:
(x-5) is negative
(x+2) is positive
Then (x+2)(x-5) is negative, so it's undefined.
So the function is defined for x>5 and x<-2
So the correct option is option D.
