KVPY Sample Paper KVPY Stream-SX Model Paper-15

The interval in which function \[f(x)={{\sin }^{-1}}({{x}^{2}}-3x+3)\] is increasing, is-

A) \[[1,2]\]

B) \[\left[ \frac{3}{2},\infty \right)\]

C) \[\left[ \frac{3}{2},2 \right]\]

D) None of these

Correct Answer: C

Solution :

\[-1\le {{x}^{2}}-3x+3\le 1\]

\[\Rightarrow {{x}^{2}}-3x+4\ge 0\] and \[{{x}^{2}}-3x+2\ge 0\]

\[\Rightarrow x\in [1,2]\]

\[f'(x)=\frac{2x-3}{\sqrt{1-{{({{x}^{2}}-3x+3)}^{2}}}}\ge 0\Rightarrow x\ge \frac{3}{2}\]