Functions Question 710
Question: Inverse of the function $ f:R\to (-\infty ,1) $ given by $ f(x)=1-{2^{-x}} $ is
Options:
A) $ -{\log_2}(1-x) $
B) $ -{\log_2}(x) $
C) 0
D) 1
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let $ y=1-{2^{-x}}or{2^{-x}}=1-y $ or $ -x={\log_2}(1-y)or{f^{-1}}(x)=g(x)=-log_2(1-x). $