Why is x > = 0 when finding the inverse function of hyperbolic cosine function y = CHX?

Why is x > = 0 when finding the inverse function of hyperbolic cosine function y = CHX?

Y = ln (x ± √ x ^ 2-1). If y is not equal to or greater than 0, y has two values

The relationship between hyperbolic sine, hyperbolic cosine and hyperbolic tangent

The relationship between hyperbolic sine and hyperbolic cosine is shown in the figure
 
Hope the landlord can adopt it!

The inverse function of F (x) is g (x), f (g (x)) =?

Let y = f (x), then x = g (y)
For the sake of convenience, let's write: F (g (y)) [x, y are variables, it doesn't matter how to write]
f(g(y))=f(x)=y
So:
f(g(x))=x