If the function is f (x) = ln (x+x 2), it is as follows:

Domain:

The domain of ln(X) function is X >；; 0, that is, x+x 2 > in the function of this question; 0

Solve the inequality and get the result: x>0 or X.

Monotonicity:

Deduce f (x): f' (x) = (2x+1)/(x+x 2), and then judge the relationship between this formula and 0. If it is greater than 0, it means that the original function f(x) is monotonically increasing, and vice versa.

f'(x)=(2x+ 1)/(x+x^2)>； 0

= & gt(2x+ 1)*(x+x^2)>； 0

= & gt- 1 & lt； X<- 1/2 or x >；; 0

Combined with the definition domain, the function increases monotonically in x>0 on the X axis.