Functions Question 441

Question: If $ f(x)={e^{-x}}, $ then $ \frac{f(-a)}{f(b)} $ is equal to

Options:

A) $ f(a+b) $

B) $ f(a-b) $

C) $ f(-a+b) $

D) $ f(-a-b) $

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Answer:

Correct Answer: D

Solution:

[d] $ \frac{f(-a)}{f(b)}=\frac{e^{a}}{{e^{-b}}}=e^{a}e^{b}={e^{a+b}}={e^{-(-a-b)}} $ $ =f(-a-b) $