Explanation

(c)
Since, $f:R \rightarrow R$ such that $f(x) = 3^{- x}$
Let $y_{1}$ and $y_{2}$ be two elements of $f(x)$ such that $y_{1} = y_{2}$
$\Rightarrow \ \ \ \ \ \ \ 3^{- x_{1}} = 3^{- x_{2}}\ \Rightarrow \ \ \ \ x_{1} = x_{2}$
Since, if two images are equal, then their elements are equal, therefore it is one-one function.
Since, $f(x)$ is positive for every value of $x$, therefore $f(x)$ in into.
On differentiating w.r.t. $x$, we get $\frac{dy}{dx} = - 3^{- x}\log{3 < 0}$ for every value of $x$.
$\therefore$ It is decreasing function.
$\therefore$ Statement I and II are true.