How do you determine if #f(x)=6x-root3x# is an even or odd function?

1 Answer
George C.
Apr 10, 2016

This #f(x)# is an odd function since #f(-x) = -f(x)# for any #x#.

Explanation:

#f(x)# is an even function if #f(-x) = f(x)# for any #x#

#f(x)# is an odd function if #f(-x) = -f(x)# for any #x#

For any value of #x# we have:

#f(-x) = 6(-x)-root(3)(-x) = -6x+root(3)(x) = -(6x-root(3)(x)) = -f(x)#

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

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