Before coming to the domain range difficulty just have another look at
-sqr(x) = y
It should be sqr(-x) = y
Now you can choose a domain for a function. It is not pre-defined by the function.
For example
y = 2x. I can have domain = {counting numbers} or domain = {integers} or domain = {real numbers} etc etc.
So why would a book say
domain of x = -y^2 = (-infinity, 0]
Well if x is positive then the square root takes you into complex numbers. Nothing wrong with that but your book has chosen not to. By picking any negative number and zero, the book makes sure that y is real.
Now about the range.
If I define a function as y = sqr(-x), then any mathematician is entitled to ask, which square root am I supposed to take (+ or -) because a function must be well defined ... that is to say, have just one value of y for any x we choose.
But the function you started with isn't defined like that.
It is defined 'backwards' ie. x = -y^2
Does that make any difference?
So we choose an x in the domain (let's say x = -9) and try to find a y to fit. I can find two values that work y = + 3 and y = -3. So I guess that's why the book wants the range to be -infinity to + infinity.
But I'm with you on this.
The book range means it isn't a well defined function as it has two values of y for any x (not equal to zero).
I like your range better
R(-infinity, 0]
But you are implying that the negative square root should be taken. Again, nothing wrong with that, but some people might wonder why you didn't have (0,+infinity]. This is also possible until we get clarity on the square root.
Bob
]]>Welcome to the forum! I solved it like this obviously.
The square takes precedence so - y^2 = - (y^2).
I assumed x >=0 so I did not put the plus minus in front. Anyway it was not necessary to solve it and did not want to confuse him with ± i.
You might be right about the lack of rigor of that problem but I rarely argue with their teachers or their textbooks. I just try to guess what they want.
This is my first post here and I do not yet know how to make equations look good.
Here is where you go to start learning latex.
http://www.mathisfunforum.com/viewtopic.php?id=4397
If you are lazy like me then you can go here and this page will do it for you.
]]>But that is not important.
Domain = ( -∞, 0] and the Range is (-∞,∞)
]]>I'm getting D[0,infinity) and R(-infinity, 0]
]]>Solve that equation for y and then do the domain and range, tell me what you get.
]]>x = -y^2
A textbooks tells me the domain of x = -y^2 = (-infinity, 0] and the range is (-infinity, infinity)
But, its not clicking how they get this
I'm getting D[0,infinity) and R(-infinity, 0]
]]>