csat-suneung· South-Korea· csat__math-science4 marks
The graph of the function $y = f ( x )$ defined on the open interval $( - 2,2 )$ is shown in the following figure. On the open interval $( - 2,2 )$, define the function $g ( x )$ as $$g ( x ) = f ( x ) + f ( - x )$$ Which of the following in are correct? [4 points] ㄱ. $\lim _ { x \rightarrow 0 } f ( x )$ exists. ㄴ. $\lim _ { x \rightarrow 0 } g ( x )$ exists. ㄷ. The function $g ( x )$ is continuous at $x = 1$. (1) ᄂ (2) ᄃ (3) ᄀ, ᄂ (4) ᄀ, ᄃ (5) ᄂ, ᄃ
The graph of the function $y = f ( x )$ defined on the open interval $( - 2,2 )$ is shown in the following figure.
On the open interval $( - 2,2 )$, define the function $g ( x )$ as
$$g ( x ) = f ( x ) + f ( - x )$$
Which of the following in <Remarks> are correct? [4 points]
\textbf{<Remarks>}\\
ㄱ. $\lim _ { x \rightarrow 0 } f ( x )$ exists.\\
ㄴ. $\lim _ { x \rightarrow 0 } g ( x )$ exists.\\
ㄷ. The function $g ( x )$ is continuous at $x = 1$.\\
(1) ᄂ\\
(2) ᄃ\\
(3) ᄀ, ᄂ\\
(4) ᄀ, ᄃ\\
(5) ᄂ, ᄃ