What is the domain of the function y = lgx ^ 2? Ar B (0, positive infinity) C (negative infinity, 0) d {x | x is not equal to 0}

What is the domain of the function y = lgx ^ 2? Ar B (0, positive infinity) C (negative infinity, 0) d {x | x is not equal to 0}

True number x & # 178; > 0
x≠0
Choose D

It is proved that arctan x ≤ x when x > 0

Let f (x) = arctan X-X
f'(x)=1/(1+x^2)-1=-x^2/(1+x^2)
When x > 0
f'(x)=x^2/(1+x^2)＜0
So f (x) is monotonically decreasing
f(0)=0
When x > 0
f(x)=arctan x-x＜0
So when x > 0, arctan x < X

The monotone increasing interval of function f (x) = xlnx (x > 0) is______ ．

From the function f (x) = xlnx: F (x) = LNX + 1, Let f ′ (x) = LNX + 1 ＞ 0, that is LNX ＞ - 1 = ln1e. According to e ＞ 1, the logarithmic function is an increasing function, so x ＞ 1E is the monotone increasing interval of the function. So the answer is: (1E, + ∞)