question_answer

Let \[f(x)=\int\limits_{2}^{x}{\frac{dt}{\sqrt{1+{{t}^{4}}}}}\]      and g be the inverse of f. Then g? (0) is equal to

A)  1                                

B)  17

C)  \[\sqrt{17}\]                             

D)  0

Correct Answer: C

Solution :

\[\therefore \,\,\,g'(0)\,=\frac{1}{f'(2)}\,=\frac{1}{\left( \frac{1}{\sqrt{17}} \right)}\,=\sqrt{17}\]