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Find the inverse of the function: f: R r...

Find the inverse of the function: `f: R rarr (-oo,1)gi v e nb y\ f(x)=1-2^(-x)`

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1)(x)=-log_(2)(1-x)`
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)`
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