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If the function f:[1,oo)->[1,oo) is def...

If the function `f:[1,oo)->[1,oo)` is defined by `f(x)=2^(x(x-1)),` then `f^-1(x)` is (A) `(1/2)^(x(x-1))` (B) `1/2 sqrt(1+4log_2x)` (C) `1/2(1-sqrt(1+4log_2x))` (D) not defined

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

`y=2^(x(x-1)) or x^(2)-x-log_(2) y=0`
`or x=(1)/(2)(1+-sqrt(1+4 log_(2)y))`
Since `x in [1, oo), " we choose " x=(1)/(2)(1+sqrt(1+4 log_(2)y))`
` or f^(-1) (x) =(1)/(2)(1+sqrt(1+4 log_(2)x)).`
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