f(x) = x2-x+1/x2+x+1 find domain and range
explain too
thanks !

Dear Student,

y = x2-x+1x2+x+1
Domain is x R
For Range of function:

yx‚Äč2 + xy + y = x2 - x + 1
(y-1)x+ (y+1)x + y-1 = 0

if y = -1
-2x2 -1 -1 = 0
-2x2 -2 = 0
Therefore, y cannot be equal to -1 since x will be a complex value

Now, y not equal to -1. 
(y-1)x2 + (y+1)x + y-1 = 0   has real roots

hence, (y+1)- 4 (y-1)(y-1) 0
y2 + 2y + 1 - 4y2 + 8y - 4 0
-3y2 + 10y - 3  0
3y2 - 10y + 3 0
3y2 - 9y - y + 3  0
3y (y-3) - 1 (y-3) 0
(3y-1)(y-3)  0
13,3 
Hence, range of function is 13,3
Regards

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