Functions Question 716
Question: The inverse of $ f(x)=\frac{2}{3}\frac{10^{x}-{10^{-x}}}{10^{x}+{10^{-x}}} $ is
Options:
A) $ \frac{1}{3}{\log_{10}}\frac{1+x}{1-x} $
B) $ \frac{1}{2}{\log_{10}}\frac{2+3x}{2-3x} $
C) $ \frac{1}{3}{\log_{10}}\frac{2+3x}{2-3x} $
D) $ \frac{1}{6}{\log_{10}}\frac{2-3x}{2+3x} $
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Answer:
Correct Answer: B
Solution:
[b] if $ y=\frac{2}{3}\frac{10^{x}-{10^{-x}}}{10^{x}+{10^{-x}}},10^{2x}=\frac{3y+2}{2-3y} $ or $ x=\frac{1}{2}{\log_{10}}\frac{2+3y}{2-3y} $
$ \therefore {f^{-1}}(x)=\frac{1}{2}{\log_{10}}\frac{2+3x}{2-3x}. $
BETA
