Let $I , J$ be nonempty open intervals in $\mathbb { R }$. Let $f : I \longrightarrow J$ and $g : J \longrightarrow \mathbb { R }$ be functions. Let $h : I \longrightarrow \mathbb { R }$ be the composite function $g \circ f$. Pick the correct statement(s) from below. (A) If $f , g$ are continuous, then $h$ is continuous. (B) If $f , g$ are uniformly continuous, then $h$ is uniformly continuous. (C) If $h$ is continuous, then $f$ is continuous. (D) If $h$ is continuous, then $g$ is continuous.
Let $I , J$ be nonempty open intervals in $\mathbb { R }$. Let $f : I \longrightarrow J$ and $g : J \longrightarrow \mathbb { R }$ be functions. Let $h : I \longrightarrow \mathbb { R }$ be the composite function $g \circ f$. Pick the correct statement(s) from below.\\
(A) If $f , g$ are continuous, then $h$ is continuous.\\
(B) If $f , g$ are uniformly continuous, then $h$ is uniformly continuous.\\
(C) If $h$ is continuous, then $f$ is continuous.\\
(D) If $h$ is continuous, then $g$ is continuous.