Another question on domain and range??

Question

Okay so the problem is y=the square root of x+17

x cannot equal -17.

So do I use brackets or parenthesis. Thank you to everyone who answered my first question, but I don't understand how you would know that -17 IS included or IS NOT included.

Answer 1

No No, under a square root the number must be greater or equal to zero.

y=sqrt(x+17)

so x+17>=0 ==> x>=-17
where >= means greater or equal

==> you write:

Domain of x is: [-17,inf[

-17 is included !!
inf means infinity and there you put an open bracket.

Range of y is [0, inf[


****** Open and Closed Brackets ** ** * * *

An open bracket is used when a number is not included in the solution
example:

x>0 can also be written: x belongs to ] 0 , inf [

Closed brackets are used when the number is included in the solution
example:
x>=0 x belongs to [0,inf[
at inf you always put open bracket

Answer 2

x = -17 is acceptable, because sqrt(-17 + 17) = sqrt(0) = 0. If x < -17, then x + 17 < 0, and we don't want a negative number under a square root operator. Any number >= -17 is okay, so that is your domain. The range (the set of all values y which the function can take) is the set of all nonnegative real numbers.

I don't understand your query about brackets or parens.

Answer 3

I see where your difficulty lies...

The value which is to be square-rooted cannot be negative.

This can be explained through the inverse operation of a square.

The square of 3 is 9, since square root is the "inversed" operation of the square, intuitively, the square root of 9 would be 3.

Now, any value that is squared will yield a positive value, whether it be a positive or a negative. (-3 x -3 = 9)

Therefore, it follows that the square root of a number cannot be negative.

A zero however, can be considered an answer as 0 x 0 = 0

Hope that helps ^_^