How do you determine if #f(x) = 5x^-2 - 4x^4# is an even or odd function?

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Answer 1 · 2018-04-18T10:31:41

#color(blue)("Even")#

A function is even if:

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

A function is odd if:

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

Test for even:

#f(x)=5x^(-2)-4x^4=5/(x^2)-4x^4#

#f(-x)=5(-x)^(-2)-4(-x)^4=5/((-x)^2)-4(-x)^4=5/x^2-4x^4#

#:.#

#f(x)=f(-x)# the function is even.