How do you determine whether #f(x) = 2^x + 2^-x# is an odd or even function?

1 Answer
Dec 25, 2015

#f(-x) = 2^(-x) + 2^x = 2^x+2^(-x) = f(x)#

so #f(x)# is even

Explanation:

If #f(-x) = f(x)# for all Real numbers #x# in the domain of #f(x)# then we call #f(x)# even.

If #f(-x) = -f(x)# for all Real numbers #x# in the domain of #f(x)# then we call #f(x)# odd.

In our example, substituting #-x# for #x# gives the same result, so #f(x)# is even.