Mathematics

Problem

#### Passage II (Q. Nos. 91 to 94) 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

. If

h(x) = f'(x)

, then

h(x)

is given by a.

-f(x)

\frac{1}{f(x)}

f(x)

e^{f(x)}