How do you know if #(3x) / (4-x^2) # is an even or odd function?

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Answer 1 · 2016-09-14T05:42:50

#(3x)/(4-x^2)# is an odd function.

A function #f(x))# is even if #f(-x)=f(x)# and is odd if #f(-x)=-f(x)#.

It is also possible that it is neither.

As here #f(x)=(3x)/(4-x^2)#

#f(-x)=(3xx(-x))/(4-(-x)^2)#

= #(-3x)/(4-x^2)#

= #-(3x)/(4-x^2)#

= #-f(x)#

Hence #(3x)/(4-x^2)# is an odd function.