Functions Question 533
Question: If $ f(x)=5log_5x $ then $ {f^{-1}}(\alpha -\beta ) $ where $ \alpha ,\beta \in R $ is equal to
Options:
A) $ {f^{-1}}(\alpha )-{f^{-1}}(\beta ) $
B) $ \frac{{f^{-1}}(\alpha )}{{f^{-1}}(\beta )} $
C) $ \frac{1}{f(\alpha -\beta )} $
D) $ \frac{1}{f(\alpha )-f(\beta )} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ f(x)=5log_5x\Rightarrow {f^{-1}}(x)={5^{5/x}} $ $ {f^{-1}}(\alpha -\beta )={5^{\frac{\alpha -\beta }{5}}}=\frac{{5^{\alpha /5}}}{{5^{\beta /5}}}=\frac{{f^{-1}}(\alpha )}{{f^{-1}}(\beta )} $
BETA
