1. ## 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.

2. An even funtion satisfies $\displaystyle f(x)=f(-x).$ In the same fashion of your other problem (odd hyperbolic sin function), do it.

3. 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.

4. ## Are you..

Originally Posted by Krizalid
An even funtion satisfies $\displaystyle f(x)=f(-x).$ 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?

5. ## Then....

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?