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How do you determine if #h(x)=e^(|x|)# is an even or odd function?

1 Answer

May 22, 2016

Observe that #h(-x) = h(x)# to find that it is even.

Explanation:

A function #f(x)# is even if #f(-x) = f(x)# and is odd if #f(-x) = -f(x)#. Thus, to check whether #h(x)# is even or odd, we examine #h(-x)#.

#h(-x) = e^|-x| = e^|x| = h(x)#

As #h(-x) = h(x)#, #h(x)# is an even function.

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