Problem 24E

Let f: R → R and let f(x) > 0 for all .x ∈ R. Show that f(x) is strictly increasing if and only if the function g(x) = 1 /f(x) is strictly decreasing.

Solution :

Step 1:

In this problem we have to show that f(x) is strictly increasing if and only if the function g(x) = 1/f(x) is strictly decreasing .