E x is an increasing function.
E (-x) is a decreasing function.
X, x 2+1under the radical sign are all increasing function.
Lnx is increasing function, and if f(x) is increasing function, then X+√ (X 2+ 1) in ln is monotonically increasing.
g(x)=x+√(x^2+ 1)
G' (x) = 1+2x Shang G' (x) > 0
It needs to be proved on [0,1]1> x/√ (x 2+1).
Authentication on [0, 1] √ (x 2+ 1) > X is required.
It needs to be proved on [0, 1] x 2+ 1 > x 2.
It needs to be proved on [0, 1] 1 > 0.
Clearly established