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If the function f:[1,oo)to[1,oo) is defi...

If the function `f:[1,oo)to[1,oo)` is defined by `f(x)=2^(x(x-1))` then `f^(-1)` is

A

`((1)/(2))^(x(x-1))`

B

`(1)/(2)(1+sqrt(1+4log_(2)x))`

C

`(1)/(2)(1-sqrt(1-4log_(2)x))`

D

Not defined

Text Solution

Verified by Experts

The correct Answer is:
B
Given `f(x)=2^(x(x-1)) implies x(x-1) = log_2 f(x)`
`implies x^2 - x - log_2f(x)=0implies x= (1+-sqrt(4log_2f(x)))/2`
Only `f^-1(x)(1)/(2)(1+sqrt(1+4log_(2)x))`lies in the domain
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  • Let f:[4,oo)to[4,oo) be defined by f(x)=5^(x^((x-4))) .Then f^(-1)(x) is

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