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