Find the range of the function $f(x) = \arctan x + \frac{1}{2} \arcsin x.$  All functions are in radians.
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<|im_start|>user
Find the range of the function $f(x) = \arctan x + \frac{1}{2} \arcsin x.$  All functions are in radians.
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user
\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]
Find the range of the function $f(x) = \arctan x + \frac{1}{2} \arcsin x.$  All functions are in radians.
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