Question

Show that , y= log(1+x)- 2x/(2+x),x > =1,is an increasing function of x throughout its domain.

Answer 1

We have,

Since x > −1, point x = 0 divides the domain (−1, ∞) in two disjoint intervals i.e., −1 < x < 0 and x > 0.
When −1 < x < 0, we have:

Hence, function f is increasing throughout this domain.