How to find the range of #x^2/(1x^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/(1x^2)#
and solve for
Multiplying both sides by
#yyx^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 is#y >= 0# 
#y <= 0" "# and#" "y + 1 < 0# . That is#y < 1#
So the range of
graph{x^2/(1x^2) [10, 10, 5, 5]}