Problem

Part I Multiple Choice

2. A function $f$ on $\mathbb{R}$ is odd if $f(-x)=-f(x)$ for all $x\in\mathbb{R}$ while it is even if $f(-x)=f(x)$ for all $x\in\mathbb{R}$. Suppose that $g$ and $h$ are two functions on $\mathbb{R}$.

(a) If $g$ is an even function, then the composite function $h\circ g$ must be even.

(b) If $g$ is an odd function and $\lim_{x\to 0^+}g(x)=3$, then the limit $\lim_{x\to 0^-}g(x)$ must be $-3$.

(c) If $g$ is an even function and $\lim_{x\to 0^+}g(x)=3$, then the limit $\lim_{x\to 0^-}g(x)$ must be $3$.

Among the above three statements, how many of them are true?

A) Only one.

B) Only two.

C) All of them.

D) None of them.