Is the function #f(x)=x^4-6^-4+3x^2# even, odd or neither?

1 Answer
Jun 18, 2018

Answer:

The function #f# is even.

Explanation:

An even function #f# is defined such that #f(-x)=f(x)# for all #x# in the domain of #f#. Using this definition, we examine #f(-x)#:
#f(-x)=(-x)^4-6^-4+3(-x)^2#
#f(-x)=x^4-6^-4+3x^2#
#f(-x)=f(x)#
Since #f(-x)=f(x)#, we have shown that the function #f# is indeed even.