Let I be any interval disjoint from (−1, 1). Prove that the function f given by
f(x)=x+1/x is strictly increasing on I.
We have,
The points x = 1 and x = −1 divide the real line in three disjoint intervals i.e.,
Hence, function f is strictly increasing in interval I disjoint from (−1, 1).
Hence, the given result is proved.
