그래프로 합성함수 극한

ㄱ) $\displaystyle \lim\limits _{x \rightarrow \pm 0} {( f \circ f ) ( x )} = \lim\limits _{t \rightarrow 2 +} {f ( t ) = 3}$ $\uparrow$ $f ( x ) = t$ $\displaystyle \therefore \lim\limits _{x\rightarrow 0{( f \circ f ) ( x ) = 3 \ne 2}}$ ㄴ) $\displaystyle \lim\limits _{x \rightarrow 1 -} {( f \circ f ) ( x )} = \lim\limits _{t \rightarrow 3 -} {f ( t )} = 3$ $\uparrow$$f ( x ) = t$ $\displaystyle \lim\limits _{x \rightarrow 2 +} {( f \circ f ) ( x )} = \lim\limits _{t \rightarrow 3 -} {f ( t )} = 3$ $\uparrow$$f ( x ) = t$ $\displaystyle \therefore \lim\limits _{x \rightarrow 1 -} {( f \circ f ) ( x ) = \lim\limits _{x \rightarrow 2 +} {( f \circ f ) ( x ) = 3}}$ ㄷ) $( f \circ f ) ( 3 ) =$$f ( 2 ) = 3$ $\displaystyle \lim\limits _{x \rightarrow \pm 3} {( f \circ f ) ( x )} = \lim\limits _{t \rightarrow 2 +} {f ( t ) = 3}$ $\uparrow$ $f ( x ) = t$ $\displaystyle \therefore \lim\limits _{x\rightarrow 3{( f \circ f ) ( x ) = ( f \circ f ) ( x ) = 3}}$ 그러므로 옳은 것은 ㄴ과 ㄷ이다.