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$1.$ Which of the following is true?
$(A)$ $g$ is increasing on $(1, \infty)$
$(B)$ $g$ is decreasing on $(1, \infty)$
$(C)$ $g$ is increasing on $(1,2)$ and decreasing on $(2, \infty)$
$(D)$ $g$ is decreasing on $(1,2)$ and increasing on $(2, \infty)$
$2.$ Consider the statements :
$P$ : There exists some $x \in \operatorname{IR}$ such that $f(x)+2 x=2\left(1+x^2\right)$
$Q$ : There exists some $x \in \operatorname{IR}$ such that $2 f(x)+1=2 x(1+x)$ Then
$(A)$ both $P$ and $Q$ are true
$(B)$ $P$ is true and $Q$ is false
$(C)$ $P$ is false and $Q$ is true
$(D)$ both $P$ and $Q$ are false
Give the answer question $1$ and $2.$
Let $f(x)=\left\{\begin{array}{cc}\frac{x}{|x|} g(x), & x \neq 0 \\ 0, & x=0\end{array}\right.$
and $h(x)=e^{\text {ld }}$ for all $x \in R$. Let $( f \circ h )(x)$ denote $f(h(x))$ and $( h \circ f )( x )$ denote $h(f(x))$. Then which of the following is (are) true?
$(A)$ $f$ is differentiable at $x=0$
$(B)$ $h$ is differentiable at $x=0$
$(C)$ $f \circ h$ is differentiable at $x=0$
$(D)$ $h \circ f$ is differentiable at $x=0$