Hyperbolic Functions Proof

Anyone able to help with the attached question?

I've had a go at the first part, but not sure if what I've done is correct (no info in my textbook). And not really sure about the second part.

(using a second-hand book, looks like the previous person wrote over the question, typo in the book I guess)

Your working for the first part looks correct, but would be more convincing as a proof if you listed the steps in the opposite order.
For the second part, use the fact that e^(ln(f(x)) = f(x) and apply that to the given expression.

Came back to this question and still struggling - just wondering what you meant by doing it in the opposite order?

I've tried part ii (working attached) but end up with an expression that will end up multiplying roots together, so need binomial series - is this right?

For part (i) your proof reads as though you have stated that arsinh(x) > arcosh(x) and have gone on to show that, therefore, 1 > -1. This just seems to me to be back to front.

Do you mean it should be 1 < -1 or the proof should be the opposite way around?