How do you determine if #f(t)= ( t^4 tan t ) / (2 + cos t)# is an even or odd function?

1 Answer
George C.
Apr 14, 2016

Find #f(-t) = -f(t)# for any #t#, so #f(t)# is an odd function.

Explanation:

An even function satisfies #f(-x) = f(x)# for all #x# in its domain.

An odd function satisfies #f(-x) = -f(x)# for all #x# in its domain.

In our example:

#f(-t) = ((-t)^4 tan (-t))/(2 + cos (-t))#

#=(t^4 *(-tan(t)))/(2+cos(t))#

#=-(t^4 tan t)/(2 + cos t)#

#=-f(t)#

So #f(t)# is an odd function.

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