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For all integers $x>0$, let $f(x)$ be defined as $f(x)=\frac{f(x-1)}{(-1)^x}$. If $f(1)=1$, which of the following statement is correct for the values of $f(x)$?$\newline$A) The values of $f(x)$ for all even values of $x$ is the same.$\newline$B) The value of $f(x)$ for all odd values of $x$ is the same.$\newline$C) The value of $f(x)$ for all even values is $f(x)$$0$ and for all odd values is $f(x)$$1$$\newline$D) The value of $f(x)$ is either $f(x)$$0$ or $f(x)$$1$