Find the range of the function \(f(x) = \arctan x + \frac{1}{2} \arcsin x.\) All functions are in radians.
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].
Sorry,the answer was\( \boxed{\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]}\) .I don't know how they got that. But, good try.
