Question

Determine if the following are odd, even, or neither.

1. f(x)=3x^4+x^2+1

2. f(x)=x^4-3x^3+x

Answer 1

`f(x)=3x^4+x^2+1\\ f(-x)=3\cdot(-x)^4+(-x)^2+1=3x^4+x^2+1\\ f(-x)=f(x)\Rightarrow \text{ even}\\\\\\ f(x)=x^4-3x^3+x\\ f(-x)=(-x)^4-3\cdot(-x)^3-x=x^4+3x^3-x\\ f(-x)\\ot = f(x)\Rightarrow \text{ not even}\\\\ -f(x)=-(x^4-3x^3+x)=-x^4+3x^3-x\\ -f(x)\\ot=f(-x)\Rightarrow \text{ not odd}\\\Downarrow\\ \text{neither}`