$Thefunctionf:R\to Risdefinedbyf\left(x\right)=3^{-x}.Observethefollowingstatementsonit$

I) f is one - one      II) f is onto         III) f is a decreasing function

Out of these, true statements are

$\begin{array}{l}f\left(x\right)=3^{-x}andf:R\to R\\ Let{x}_1,x_2\in Randf\left(x_1\right)=f\left(x_2\right)\\ \Rightarrow 3^{-x_1}=3^{-x_2}\\ \Rightarrow -x_1=-x_2\Rightarrow x_1=x_2\\ \therefore fisone-one\\ letf\left(x\right)=y\Rightarrow 3^{-x}=y\\ \Rightarrow -x={\log }_3^y\\ \Rightarrow x=-{\log }_3^y\end{array}$

$\begin{array}{l}isdefinesify>0\\ Range=(0,\infty )=codomain\\ fisnotonto\\ f\left(x\right)=3^{-x}\Rightarrow f^{-1}\left(x\right)=-3^{-x}\log 3<0\\ \therefore fisdecrea\sin gfunction.\end{array}$