How do I show that f is strictly decreasing on (0, infinity)? I have been asked to define $f: (0, \infty) \to (0, \infty)$ by $f(x) = \frac 1 x$
a) How do I show that f is strictly decreasing on $(0, \infty)$? I realize that I have to show that $f'(x)<0$, but I'm not entirely sure how to go about this. Would anyone be able to help or point me in the right direction?
b) How do I show that $f$ is invertible, and find $f^{-1}$? Do I switch $x$ and $y$ and solve for $y$?

b) $f$ is a strictly decreasing continuous function on $(0,\infty)$, so it is surely invertible. The image is $(0,\infty)$ as given. Yes, you can swith $x$ and $y$ to find $f^{-1}$. To find the domain and image of $f^{-1}$, you can as well swith the domain and range of $f$. 
