If the function \[f:[1,\ \infty )\to [1,\ \infty )\] is defined by \[f(x)={{2}^{x(x-1)}},\] then \[{{f}^{-1}}\](x) is [IIT 1999]

\[\frac{1}{2}(1-\sqrt{1+4{{\log }_{2}}x})\]

\[{{\left( \frac{1}{2} \right)}^{x(x-1)}}\]

\[\frac{1}{2}(1+\sqrt{1+4{{\log }_{2}}x})\]

If the function \[f:[1,\ \infty )\to [1,\ \infty )\] is defined by \[f

1.	If the function \[f:[1,\ \infty )\to [1,\ \infty )\] is defined by \[f(x)={{2}^{x(x-1)}},\] then \[{{f}^{-1}}\](x) is [IIT 1999]
A.	\[{{\left( \frac{1}{2} \right)}^{x(x-1)}}\]
B.	\[\frac{1}{2}(1+\sqrt{1+4{{\log }_{2}}x})\]
C.	\[\frac{1}{2}(1-\sqrt{1+4{{\log }_{2}}x})\]
D.	Not defined
Answer» C. \[\frac{1}{2}(1-\sqrt{1+4{{\log }_{2}}x})\]

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If the function \[f:[1,\ \infty )\to [1,\ \infty )\] is defined by \[f(x)={{2}^{x(x-1)}},\] then \[{{f}^{-1}}\](x) is [IIT 1999]

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