94.9k views
0 votes
Please give an explanation.

Please give an explanation.-example-1

1 Answer

3 votes

Answer:

option D

Explanation:

So we know that
√(a) √(b) = √(ab)

Applying this to our function, we have that:


√((x-5)) √((x+2)) = √((x+2)(x-5))

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.

User Gigg
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories