Ques 1) Find the range :-

f(x) = Sin ^-1 [x² + 1/2] + Cos ^-1 [x² - 1/2]

where [.] denotes the greatest Integer function

x²-0.5>-1 and is less than x²+ (1/2)<2,therefore x²<3/2,

 for 0≤x²<1/2, f(x)=arcsin(0) +arccos(-1) =π, for 1/2≤x²<3/2, f(x) = arcsin(1)+arccos(0)=π

therefore, range is π

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