gaokao 2018 Q12

gaokao · China · national-I-arts 5 marks Composite & Inverse Functions Determine Domain or Range of a Composite Function
Let $f ( x ) = \begin{cases} 2 ^ { -x } & x \leq 0 \\ 1 & x > 0 \end{cases}$. Then the range of $x$ satisfying $f ( x + 1 ) < f ( 2 x )$ is
A. $( - \infty , - 1 ]$
B. $( 0 , + \infty )$
C. $( - 1,0 )$
D. $( - \infty , 0 )$
Let $f ( x ) = \begin{cases} 2 ^ { -x } & x \leq 0 \\ 1 & x > 0 \end{cases}$. Then the range of $x$ satisfying $f ( x + 1 ) < f ( 2 x )$ is

A. $( - \infty , - 1 ]$\\
B. $( 0 , + \infty )$\\
C. $( - 1,0 )$\\
D. $( - \infty , 0 )$