(Calculus) For the function $f ( x ) = x + \sin x$, define the function $g ( x )$ as $$g ( x ) = ( f \circ f ) ( x )$$ Which of the following in are correct? [3 points] ㄱ. The graph of function $f ( x )$ is concave down on the open interval $( 0 , \pi )$. ㄴ. The function $g ( x )$ is increasing on the open interval $( 0 , \pi )$. ㄷ. There exists a real number $x$ in the open interval $( 0 , \pi )$ such that $g ^ { \prime } ( x ) = 1$. (1) ᄀ (2) ᄃ (3) ᄀ, ᄂ (4) ᄂ, ᄃ (5) ᄀ, ᄂ, ᄃ
(Calculus) For the function $f ( x ) = x + \sin x$, define the function $g ( x )$ as
$$g ( x ) = ( f \circ f ) ( x )$$
Which of the following in <Remarks> are correct? [3 points]
\textbf{<Remarks>}\\
ㄱ. The graph of function $f ( x )$ is concave down on the open interval $( 0 , \pi )$.\\
ㄴ. The function $g ( x )$ is increasing on the open interval $( 0 , \pi )$.\\
ㄷ. There exists a real number $x$ in the open interval $( 0 , \pi )$ such that $g ^ { \prime } ( x ) = 1$.\\
(1) ᄀ\\
(2) ᄃ\\
(3) ᄀ, ᄂ\\
(4) ᄂ, ᄃ\\
(5) ᄀ, ᄂ, ᄃ