For a polynomial function $f ( x )$, define the function $g ( x )$ as follows: $$g ( x ) = \begin{cases} x & ( x < - 1 \text{ or } x > 1 ) \\ f ( x ) & ( - 1 \leq x \leq 1 ) \end{cases}$$ For the function $h ( x ) = \lim _ { t \rightarrow 0 + } g ( x + t ) \times \lim _ { t \rightarrow 2 + } g ( x + t )$, which of the following statements in the given options are correct? [4 points] ㄱ. $h ( 1 ) = 3$ ㄴ. The function $h ( x )$ is continuous on the set of all real numbers. ㄷ. If the function $g ( x )$ is decreasing on the closed interval $[ - 1, 1 ]$ and $g ( - 1 ) = - 2$, then the function $h ( x )$ has a minimum value on the set of all real numbers. (1) ㄱ (2) ㄴ (3) ㄱ, ㄴ (4) ㄱ, ㄷ (5) ㄴ, ㄷ
For a polynomial function $f ( x )$, define the function $g ( x )$ as follows:
$$g ( x ) = \begin{cases} x & ( x < - 1 \text{ or } x > 1 ) \\ f ( x ) & ( - 1 \leq x \leq 1 ) \end{cases}$$
For the function $h ( x ) = \lim _ { t \rightarrow 0 + } g ( x + t ) \times \lim _ { t \rightarrow 2 + } g ( x + t )$, which of the following statements in the given options are correct? [4 points]
ㄱ. $h ( 1 ) = 3$\\
ㄴ. The function $h ( x )$ is continuous on the set of all real numbers.\\
ㄷ. If the function $g ( x )$ is decreasing on the closed interval $[ - 1, 1 ]$ and $g ( - 1 ) = - 2$, then the function $h ( x )$ has a minimum value on the set of all real numbers.\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄴ\\
(4) ㄱ, ㄷ\\
(5) ㄴ, ㄷ