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What is the domain of #f(x)= arcsin[sqrt(x)]#?

Answer 1

The domain of #f(x)# is #x<=1#

As the range for #sin(x)# is #[-1,1]# for all real #x#

So, if we simplify the above equation:

#f(x)=arcsin(sqrt(x))# ;or #sin(f(x))=sqrt(x)# ;or So, we know that the range of above equation is #[-1,1]# thus, #sqrt(x)# is #[-1,1]# ;or #x<=1# is the solution or the domain of the original #f(x)#

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Answer 2

Brooklyn Anderson

The domain of ( f(x) = \arcsin(\sqrt{x}) ) is ( x \geq 0 ), because the square root of a non-negative number is real, and the arcsin function is defined for values between -1 and 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.