Let be a function that is differentiable everywhere and that has the following…

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

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 (1) odd (2) even (3) increasing (4) decreasing