- #1

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why is the alternate form of arccosh(x) = log(x + sqrt(x^2 - 1)) and not log(x - sqrt(x^2 - 1))

How do I justify the plus/minus sign?

I need to know this ASAP, thanks.

- Thread starter nehcrow
- Start date

- #1

- 15

- 0

why is the alternate form of arccosh(x) = log(x + sqrt(x^2 - 1)) and not log(x - sqrt(x^2 - 1))

How do I justify the plus/minus sign?

I need to know this ASAP, thanks.

- #2

Mentallic

Homework Helper

- 3,798

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If we were to use the minus sign then [tex]0<x-\sqrt{x^2-1}<1[/tex] for [tex]x>1[/tex] and the log of this is a negative value. To have an inverse

why is the alternate form of arccosh(x) = log(x + sqrt(x^2 - 1)) and not log(x - sqrt(x^2 - 1))

How do I justify the plus/minus sign?

I need to know this ASAP, thanks.

- #3

- 15

- 0

Thank you so much!

- #4

Mentallic

Homework Helper

- 3,798

- 94

You're welcome

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