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) none of these
Correct Answer: B
Solution :
[b]: Here \[f(x)={{2}^{x(x-1)}}=y(say)\] \[\Rightarrow \]\[{{\log }_{2}}y=x(x-1)lo{{g}_{2}}2\] \[\Rightarrow \]\[x(x-1)-lo{{g}_{2}}y=0\] \[\Rightarrow \]\[{{x}^{2}}-x-{{\log }_{2}}y=0\]\[\Rightarrow \]\[x=\frac{1\pm \sqrt{1+4{{\log }_{2}}y}}{2}\] \[\Rightarrow \text{ }x=\frac{1+\sqrt{1+4{{\log }_{2}}y}}{2}\,\,\,\,\,(\because x>1)\] \[\therefore \]\[{{f}^{-1}}(x)=\frac{1}{2}\left( 1+\sqrt{1+4{{\log }_{2}}x} \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
