Đáp án:
a) Hàm số đồng biến trên R khi:
$\begin{array}{l}
2 - m > 0\\
\Rightarrow m < 2
\end{array}$
b)
$\begin{array}{l}
- cho\,x = 0 \Rightarrow y = 1\\
\Rightarrow B\left( {0;1} \right)\\
\Rightarrow OB = 1\\
- cho\,y = 0 \Rightarrow x = \dfrac{1}{{m - 2}}\left( {m \ne 2} \right)\\
\Rightarrow A\left( {\dfrac{1}{{m - 2}};0} \right)\\
\Rightarrow OA = \dfrac{1}{{\left| {m - 2} \right|}}\\
\Rightarrow {S_{OAB}} = \dfrac{1}{2}.OA.OB\\
= \dfrac{1}{2}.\dfrac{1}{{\left| {m - 2} \right|}}.1 = 2\\
\Rightarrow \left| {m - 2} \right| = \dfrac{1}{4}\\
\Rightarrow \left[ \begin{array}{l}
m - 2 = \dfrac{1}{4}\\
m - 2 = - \dfrac{1}{4}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
m = \dfrac{9}{4}\\
m = \dfrac{7}{4}
\end{array} \right.
\end{array}$
