Free SAT Practice Question

Question 1 of 1
ID: SAT-PTAM-4
Section: Math - Passport to Advanced Math
Topics: Functions; Pattern of values
Difficulty level: Hard

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For all integers $x>0$, let $f\left(x\right)$ be defined as $f\left(x\right)=\dfrac{f\left(x - 1\right)}{{\left(-1\right)}^x}$. If $f\left(1\right)=1$, which of the following statement is correct for the values of $f\left(x\right)$? (without calculator)

AThe values of $f\left(x\right)$ for all even values of $x$ is same.
BThe values of $f\left(x\right)$ for all odd values of $x$ is same.
CThe values of $f\left(x\right)$ for all even values of $x$ is 1 and that for all odd values of $x$ is $-1$.
DThe values of $f\left(x\right)$ is either 1 or $-1$.
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