If the function `f:(1,oo)rarr(1,oo)` is defined by `f(x)=2^(x(x-1)),t h e nf^(-1)(x)` is
`(a) (1/2)^(x(x-1))`
(b) `1/2(1+sqrt(1+4(log)_2x))`
`(c)1/2(1-sqrt(1+(log)_2x)`
(d) not defined

Explanation

`f(x)=2^{x(x-1)} text {, i.e., } y=2^{x(x+1)}`


`Rightarrow log _{2} y=x(x-1)=x^{2}-x `


`Rightarrow x^{2}-x-log _{2} y=0 `


`Rightarrow x=frac{1=sqrt{1+4 log _{2} y}}{2}`



Since `x in[1, infty)` quad therefore`-ve` sign is ruled out.



`therefore Rightarrow x=frac{1}{2}(1+sqrt{1+4 log _{2} y})`


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