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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 range fo the function `Delta = f(|x|)` is

A

R

B

`R - {0}`

C

`R^(+)`

D

(0, e)

Text Solution

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The correct Answer is:
C
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