i)  State the domain and range of y = xsin^-1(x^2).


    In this problem, there are two possible partial functions/branches.


    1st possible partial function/branch:  the domain is  [0,1];  the range is [0,].

    2nd possible partial function/branch:  the domain is [-1,0];  the range is [,0].


    Both these partial functions/branches finally merge into ONE function/answer
    with the domain  [-1,1]  and  the range  [,].


    To see the plot of the final function, go to web-site www.desmos.com/calculator
    and use free of charge plotting tool there.
    Print the function expression x*arcsin(x^2) and get the plot.



2)  State the domain and range of y = tan^-1(sqrt(1-x^2)).


    In this problem, there are two possible partial functions/branches.


    1st possible function/branch:  the domain is  [0,1];  the range is [0,].

    2nd possible function/branch:  the domain is [-1,0];  the range is [0,].


    Both these partial functions/branches finally merge into ONE function/answer 
    with the domain  [-1,1]  and  the range  [0,].


    To see the plot of the final function, go to web-site www.desmos.com/calculator
    and use free of charge plotting tool there.
    Print the function expression arctan(sqrt(1-x^2)) there and get the plot.