How do you determine if #x-sin(x)# is an even or odd function?

1 Answer
May 26, 2016

Examine how it acts on #-x# to find that #f(x)=x-sin(x)# is an odd function

Explanation:

A function #f# is called even if #f(-x) = f(x)# and odd if #f(-x)=-f(x)#. Then, to determine whether the given function is even, odd, both, or neither, we examine how it acts on #-x#.

Letting #f(x) = x-sin(x)#, we have

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

#=-x-(-sin(x))#

#=-x+sin(x)#

#=-(x-sin(x))#

#=-f(x)#

Thus, #f(x)=x-sin(x)# is an odd function#