Sets Relations And Functions Question 40
Question: Which pair of functions is identical?
Options:
A) $\sin ^{-1}(\sin x)$ and $\sin (\sin ^{-1} x)$
B) $ {\log_{e}}e^{x},{e^{{\log_{e}}x}} $
C) $ {\log_{e}}x^{2},2log_{e}x $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] Here,
(1) $ {{\sin }^{-1}}(\sin x) $ is defined for $ x\in [ -\frac{\pi }{2},\frac{\pi }{2} ] $ , while $ \sin (si{n^{-1}}x) $ is defined only for $ x\in [-1,1] $
(2) $ {\log_{e}}e^{x}, $ is defined for all x, while $ {e^{{\log_{e}}x}} $ is defined for $ x>0. $
(3) $ {\log_{e}}x^{2} $ is defined for all $ x\in R-{0} $ , while $ 2{\log_{e}}x $ is defined for $ x>0. $
Thus, none is identical.
BETA
