As shown in the figure, the graph of the function $f ( x )$ defined on the closed interval $[ 0,4 ]$ is formed by connecting the points $( 0,0 ) , ( 1,4 ) , ( 2,1 ) , ( 3,4 ) , ( 4,3 )$ in order with line segments. Find the number of sets $X = \{ a , b \}$ satisfying the following condition. (Here, $0 \leq a < b \leq 4$) [4 points] A function $g ( x ) = f ( f ( x ) )$ from $X$ to $X$ exists and satisfies $g ( a ) = f ( a ) , g ( b ) = f ( b )$. (1) 11 (2) 13 (3) 15 (4) 17 (5) 19
As shown in the figure, the graph of the function $f ( x )$ defined on the closed interval $[ 0,4 ]$ is formed by connecting the points $( 0,0 ) , ( 1,4 ) , ( 2,1 ) , ( 3,4 ) , ( 4,3 )$ in order with line segments.\\
Find the number of sets $X = \{ a , b \}$ satisfying the following condition. (Here, $0 \leq a < b \leq 4$) [4 points]\\
A function $g ( x ) = f ( f ( x ) )$ from $X$ to $X$ exists and satisfies $g ( a ) = f ( a ) , g ( b ) = f ( b )$.\\
(1) 11\\
(2) 13\\
(3) 15\\
(4) 17\\
(5) 19