# Hyperbolic Cosine Function

• Nov 9th 2008, 06:45 AM
magentarita
Hyperbolic Cosine Function
The hyperbolic cosine function, designated by cosh x is defined as cosh x = (1/2) (e^x + e^(-x)).

Show that f(x) = cosh x is an even number.
• Nov 9th 2008, 08:59 AM
Krizalid
An even funtion satisfies $f(x)=f(-x).$ In the same fashion of your other problem (odd hyperbolic sin function), do it.
• Nov 9th 2008, 10:11 AM
HallsofIvy
Quote:

Originally Posted by magentarita
The hyperbolic cosine function, designated by cosh x is defined as cosh x = (1/2) (e^x + e^(-x)).

Show that f(x) = cosh x is an even number.

That is NOT what the questions asks because it makes no sense. cosh x is an even FUNCTION not an even number.
• Nov 9th 2008, 09:20 PM
magentarita
Are you..
Quote:

Originally Posted by Krizalid
An even funtion satisfies $f(x)=f(-x).$ In the same fashion of your other problem (odd hyperbolic sin function), do it.

Are you saying to replace x with -x in the given function and simplify?
• Nov 9th 2008, 09:21 PM
magentarita
Then....
Quote:

Originally Posted by HallsofIvy
That is NOT what the questions asks because it makes no sense. cosh x is an even FUNCTION not an even number.

What is the correct method for solving this question?