Question 1202942
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State the domain and range of:
i/ y = xsin^-1(x^2)
ii/ y = tan^-1(sqrt(1-x^2))
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<pre>
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,{{{pi/2}}}].

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


    Both these partial functions/branches finally merge into ONE function/answer
    with the domain  [-1,1]  and  the range  [{{{-pi/2}}},{{{pi/2}}}].


    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,{{{pi/2}}}].

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


    Both these partial functions/branches finally merge into ONE function/answer 
    with the domain  [-1,1]  and  the range  [0,{{{pi/2}}}].


    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.
</pre>

Solved.