New function of numbers

I have a function named f ( x ) f(x) such that:

{ If x can be express as 4 n + 1 then f ( x ) = 1 If x can be express as 4 n + 3 then f ( x ) = 1 If x is a even number then f ( x ) = 0 \begin{cases} \text{If }x\text{ can be express as }4n+1\text{ then }f(x)=1 \\ \text{If }x\text{ can be express as }4n+3\text{ then }f(x)=-1 \\ \text{If }x\text{ is a even number then }f(x)=0 \end{cases}

Is f ( x ) f(x) a multiplicative function?

Note

  • A "multiplicative" function means f ( a ) × f ( a ) = f ( a × a ) f(a) \times f(a')=f(a \times a') where a a and a a ' are relatively prime
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