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Find the inverse of the function: f:[1, ...

Find the inverse of the function: `f:[1, oo) rarr [1,oo),w h e r ef(x)=2^(x(x-2))`

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1)(x)=1-sqrt(1+log_(2)x)`
`y=2^(x(x-2))`
or ` x^(2)-2x=log_(2)y`
or ` x^(2)-2x-log_(2)y=0`
or `x=1+-sqrt(1+log_(2)y)`
or `f^(-1)(x)=1-sqrt(1+log_(2)x)`
as `f^(-1):[(1)/(2),oo) to (-oo,1]`
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