How to find the range of x^2/(1-x^2)?
I thought that the answer is R:(-oo,-1)uu(-1,+oo) but the book says that the correct answer is R:(-oo,-1)uu[0,+oo)
Can anyone help please?
I thought that the answer is
Can anyone help please?
1 Answer
Aug 10, 2018
The range of
Explanation:
Let:
y = x^2/(1-x^2)
and solve for
Multiplying both sides by
y-yx^2 = x^2
Adding
y = (y+1)x^2
Then dividing both sides by
x^2 = y/(y+1)
This has solutions if and only if:
y/(y+1) >= 0
That is, if either of the following:
-
y >= 0" " and" "y + 1 > 0 . That isy >= 0 -
y <= 0" " and" "y + 1 < 0 . That isy < -1
So the range of
graph{x^2/(1-x^2) [-10, 10, -5, 5]}