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

Question

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

Answer 1

Here,

f(x) = log(1 + x) - \(\frac{2x}{2+x}\) 

[Where y = f(x)]

For f(x) being increasing function

f'(x) > 0

is increasing function in its domain x > - 1.

i.e.,(-1,∞).