question_answer

Direction: Question Based on the following paragraph.

Let \[f:A\to B\]be a function defined by y=f(x) such that f is both one-one (Injective) and onto Surjective), then there exists a unique function \[g:B\to A\]such that \[f(x)=y\leftrightarrow g\] \[(y)=x,\forall x\in A\]and \[y\in B,\]then g is said to be inverse off Thus,\[g={{f}^{-1}}:B\to A=[\{f(x),x\}:\{x,f(x)\}\in {{f}^{-1}}]\] If no branch of an inverse trigonometric function is mentioned, then it means the principal value branch of that function.

If \[\frac{3\pi }{2}\le x\le \frac{5\pi }{2},\]then \[{{\sin }^{-1}}(\sin x)\]is equal to

A)  x                                

B)  x-2x

C)  \[2\pi -x\]                    

D)  -x