Question #09d6e

1 Answer
Feb 20, 2018

Read below.

Explanation:

We have:
#f(x)=(x+xcos(x))/(x-xcos(x))#

We can simplify this by factoring:

#f(x)=(x(1+cos(x)))/(x(1-cos(x))# We can cross out the #x#'s.

#f(x)=(1+cos(x))/(1-cos(x))#

Now, a function is even if:

#f(x)=f(-x)#

To try this out, we substitute all #x#'s with #-x#

#f(-x)=(1+cos(-x))/(1-cos(-x))#

Now, here is something to remember:

#sin(-x)=-sin(x)# and #cos(-x)=cos(x)#

Using this, we can say that:

#(1+cos(-x))/(1-cos(-x))=(1+cos(x))/(1-cos(x))#

Which tells us that #f(-x)=f(x)#

This means that our function is even.

When you graph this, the graph of the function will be symmetric in respect to the #y#- axis.

If #f(x)!=f(-x)#, you could check whether #f(-x)# equals #-f(x)#. If it does, than the function is odd. If it doesn't, then the function is neither even nor odd.