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Find the range of the function \(f(x) = \arctan x + \frac{1}{2} \arcsin x.\)  All functions are in radians.

 Apr 29, 2023
edited by xud33  Apr 29, 2023
edited by xud33  Apr 29, 2023
 #1
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Let y = f(x) = arctan(x) + 1/2*arcsin(x). Then y = pi/2 - 1/2*arccos(1 - x^2).  Since the range of arccos(1 - x^2) is [0,pi], the range of f(x) is [pi/4, 3*pi/4].

 Apr 29, 2023
 #2
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Sorry,the answer was\( \boxed{\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]}\) .I don't know how they got that. But, good try.

 Apr 30, 2023

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