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