A-Level Further Maths H3-02 Hyperbolic Inverse: Sketching y=arcosh(x)

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why do we disregard the negative region y=coshx?

What's stopping us from making the inverse function of coshx a reflection of the negative region of the coshx graph?

nosir
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Why do you disregard the other side of y = cosh(x) when, when doing the inverse, one output value of cosh(x) could come from a value of x on the left as well as the right?

e.g. if you’re solving cosh(x) = 2, you say x = arcosh(2) = ln(2 +- sqrt(3)), as both the plus and the minus square root are possible values of x there. Why do we discount the minus square root for arcosh(x) = ln(x +- sqrt(x^2 -))?

higaddrip