SOLUTION: can you please help me work out this problem. i need to find the range of this function: {{3+x^2/ 4-x^2}}. i tried writing the problem as two binomials on top and two binomials on

Algebra ->  Rational-functions -> SOLUTION: can you please help me work out this problem. i need to find the range of this function: {{3+x^2/ 4-x^2}}. i tried writing the problem as two binomials on top and two binomials on       Log On


   

Question 391155: can you please help me work out this problem. i need to find the range of this function: {{3+x^2/ 4-x^2}}. i tried writing the problem as two binomials on top and two binomials on the bottom and solve for x but i am not sure if that is what i am suppose to do. so can you please help me solve this problem.
Thank you so much for your time.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I will assume that your function is y+=+%283%2Bx%5E2%29%2F%284-x%5E2%29.
To find the range solve for x in terms of y and then state conditions on y that may arise.
y+=+%283%2Bx%5E2%29%2F%284-x%5E2%29
<==> 4y+-+yx%5E2+=+3+%2B+x%5E2
<==> 0+=+%281%2By%29x%5E2+-+4y+%2B+3
==> , using the quadratic formula.
Since the values of x must be real, the conditions we should impose on y are
+%281%2By%29%2A%283-4y%29%3E=+0 and y is not equal to -1.
The solution set to this inequality is the union of intervals (-infinity, -1)U[3/4, infinity). This is the RANGE of the function.