Question

f:R→(-Infinity,1) given by f(x)=1-2^-x then f^-1(x) is?​

Answer 1

$\huge\bold\pink{Solution:}$

Here,f(x) is both one -one and onto

Let y=1-2^-x Or 2^-x=1-y Or

-x=log to the base 2 (1-y) Or

f^-1(x) = g(x)= -log to the base 2 (1-x)

Answer 2

given

f (x)=1-2^x

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