For the function $$f ( x ) = \begin{cases} x + 2 & ( x < - 1 ) \\ 0 & ( x = - 1 ) \\ x ^ { 2 } & ( - 1 < x < 1 ) \\ x - 2 & ( x \geqq 1 ) \end{cases}$$ which of the following are correct? Choose all that apply from $\langle$Remarks$\rangle$. [3 points] $\langle$Remarks$\rangle$ ㄱ. $\lim _ { x \rightarrow 1 + 0 } \{ f ( x ) + f ( - x ) \} = 0$ ㄴ. The function $f ( x ) - | f ( x ) |$ is discontinuous at 1 point. ㄷ. There is no constant $a$ such that the function $f ( x ) f ( x - a )$ is continuous on the entire set of real numbers. (1) ㄱ (2) ㄱ, ㄴ (3) ㄱ, ㄷ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
For the function
$$f ( x ) = \begin{cases} x + 2 & ( x < - 1 ) \\ 0 & ( x = - 1 ) \\ x ^ { 2 } & ( - 1 < x < 1 ) \\ x - 2 & ( x \geqq 1 ) \end{cases}$$
which of the following are correct? Choose all that apply from $\langle$Remarks$\rangle$. [3 points]
$\langle$Remarks$\rangle$\\
ㄱ. $\lim _ { x \rightarrow 1 + 0 } \{ f ( x ) + f ( - x ) \} = 0$\\
ㄴ. The function $f ( x ) - | f ( x ) |$ is discontinuous at 1 point.\\
ㄷ. There is no constant $a$ such that the function $f ( x ) f ( x - a )$ is continuous on the entire set of real numbers.\\
(1) ㄱ\\
(2) ㄱ, ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ