Question

13.If sin-1 x = y, then(A) 0 y π(C) 0< y<π(D)-π < y <2

Answer 1

The inverse of a function f:A→B exists if f is one-one onto i.e.,

y=f( x )⇒ f −1 ( y )=x .

The given inverse trigonometry function is sin −1 ( x ) .

Let,

sin −1 x=y Since, the range of the principle value branch of sin -1 is [ − π 2 , π 2 ] .

Thus, − π 2 ≤y≤ π 2 is the correct option.