Determine whether each function is even, odd, or neither [/tex]f(x)=2x^3-x

Question

Determine whether each function is even, odd, or neither

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`f(x)=2x^3-x`

Answer 1

`f(x)=x^6-x^2\\ f(-x)=(-x)^6-(-x)^2=x^6-x^2\\ f(-x)=f(x) \Rightarrow \hbox{ even}\\\\ f(x)=2x^3-x\\ f(-x)=2(-x)^3-(-x)=-2x^3+x\\ f(-x)\\ot =f(x) \Rightarrow \hbox{ not even}\\ -f(x)=-(2x^3-x)=-2x^3+x\\ -f(x)=f(-x) \Rightarrow \hbox{ odd}`