The range of the function y=sin−1⁡x21+x2 is

Clearly, for y to be defined, x21+x2≤1 which is true for all x ∈ R. So, the domain = (– ∞, ∞). Now, y=sin−1⁡x21+x2⇒x21+x2=sin⁡y ⇒x=x21+x2For x to be real, sin y ≥ 0 and 1 – sin y > 0⇒0≤sin⁡y<1⇒y∈0,π2∴ Range =0,π2