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). $