+1348 Find the range of the function $$f(x) = \frac{1}{1-x} + \frac{1}{1 + x}.$$ Express your answer in interval notation.
+129771 f(x) = 1 / (1 - x) + 1/ ( 1 + x) rewrite as
f(x) = 2 / ( 1 - x^2)
Clearly, x cannot be either -1 or 1 because these two values make the denominator = 0
We have a lower power polynomial divided by a higher power polynomial....in such a case we will have a horizontal asymptote at y = 0 and it will approach -inf as x approaches -1 from the left and 1 from the right
So...part of the range is (-inf, 0)
And the function will have a minimum positive value of 2 when x = 0 and it will verge towards infinity whenever x approaches 1 from the left or -1 from the right
So...the whole range is (-inf,0) U [2, inf)
