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Let f be a function that is differentiab...

Let f be a function that is differentiable everywhere and that has the follwong properties :
(i) `f(x) gt 0`
(ii) `f'(0) = -1`
(iii) `f(-x) = (1)/(f(x))and f(x+h)=f(x).f(h)`
A standard result is `(f'(x))/(f(x))dx = log|f(x)| + C`
The function y = f(x) is

A

odd

B

even

C

increasing

D

decreasing

Text Solution

Verified by Experts

The correct Answer is:
D
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