Functions Question 124
Question: The inverse of the function $ \frac{10^{x}-{10^{-x}}}{10^{x}+{10^{-x}}} $ is
[RPET 2001]
Options:
A) $ \frac{1}{2}{\log_{10}}( \frac{1+x}{1-x} ) $
B) $ \frac{1}{2}{\log_{10}}( \frac{1-x}{1+x} ) $
C) $ \frac{1}{4}{\log_{10}}( \frac{2x}{2-x} ) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=\frac{10^{x}-{10^{-x}}}{10^{x}+{10^{-x}}}\Rightarrow x=\frac{1}{2}{\log_{10}}( \frac{1+y}{1-y} ) $ Let $ y=f(x) $
Þ $ x=\pi ,f(\pi )=-\tan \frac{\pi }{4}=-1 $
Þ $ {f^{-1}}(y)=\frac{1}{2}{\log_{10}}( \frac{1+y}{1-y} ) $
Þ $ g({{\sin }^{2}}x)=,|\sin x| $ .
BETA
