gaokao 2015 Q12

gaokao · China · national-II-arts Modulus function Solving inequalities involving modulus
12. Let $f ( x ) = \ln ( 1 + | x | ) - \frac { 1 } { 1 + x ^ { 2 } }$. The range of $x$ for which $f ( x ) > f ( 2 x - 1 )$ holds is
A. $\left( \frac { 1 } { 3 } , 1 \right)$
B. $\left( - \infty , \frac { 1 } { 3 } \right) \cup ( 1 , + \infty )$
C. $\left( - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)$
D. $\left( - \infty , - \frac { 1 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , + \infty \right)$
II. Fill-in-the-Blank Questions: This section contains 4 questions, 5 points each, 20 points total
12. Let $f ( x ) = \ln ( 1 + | x | ) - \frac { 1 } { 1 + x ^ { 2 } }$. The range of $x$ for which $f ( x ) > f ( 2 x - 1 )$ holds is\\
A. $\left( \frac { 1 } { 3 } , 1 \right)$\\
B. $\left( - \infty , \frac { 1 } { 3 } \right) \cup ( 1 , + \infty )$\\
C. $\left( - \frac { 1 } { 3 } , \frac { 1 } { 3 } \right)$\\
D. $\left( - \infty , - \frac { 1 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , + \infty \right)$

II. Fill-in-the-Blank Questions: This section contains 4 questions, 5 points each, 20 points total\\