gaokao 2021 Q12

gaokao · China · national-A-arts Function Transformations
12. Let $f ( x )$ be an odd function with domain $\mathbb{R}$, and $f ( 1 + x ) = f ( - x )$. If $f \left( - \frac { 1 } { 3 } \right) = \frac { 1 } { 3 }$, then $f \left( \frac { 5 } { 3 } \right) =$
A. $- \frac { 5 } { 3 }$
B. $- \frac { 1 } { 3 }$
C. $\frac { 1 } { 3 }$
D. $\frac { 5 } { 3 }$
II. Fill-in-the-Blank Questions: This section contains 4 questions, each worth 5 points, for a total of 20 points.
12. Let $f ( x )$ be an odd function with domain $\mathbb{R}$, and $f ( 1 + x ) = f ( - x )$. If $f \left( - \frac { 1 } { 3 } \right) = \frac { 1 } { 3 }$, then $f \left( \frac { 5 } { 3 } \right) =$\\
A. $- \frac { 5 } { 3 }$\\
B. $- \frac { 1 } { 3 }$\\
C. $\frac { 1 } { 3 }$\\
D. $\frac { 5 } { 3 }$

\section*{II. Fill-in-the-Blank Questions: This section contains 4 questions, each worth 5 points, for a total of 20 points.}