Functions Question 387
Question: If $ 3f(x)-f( \frac{1}{x} )=\log x^{4}, $ then $ f({e^{-x}}) $ is
Options:
A) $ 1+x $
B) $ 1/x $
C) $ x $
D) $ -x $
Show Answer
Answer:
Correct Answer: D
Solution:
$ 3f(x)-f( \frac{1}{x} )=\log x^{4};x\ne \frac{1}{x} $ $ 3f( \frac{1}{x} )-f(x)=\log{{( \frac{1}{x} )}^{4}} $ After solving we get $ f(x)=\log|x| $ $ f({e^{-x}})=\log_{e}{e^{-x}}=-x $
BETA
