Mathematics

Problem

Let

f

be a function that is differentiable everywhere and that has the following properties : -

f(x) > 0

f'(0) = -1

f(-x) = \frac{1}{f(x)}

and

f(x+h) = f(x) \cdot f(h)

A standard result is

\int \frac{f'(x)}{f(x)} dx = \log |f(x)| + C

. The function

y = f(x)

is a. odd b. even c. increasing d. decreasing