If u times x is equal to negative 2 x squared plus 3 and v times x is equal to 1 over x , what is the range of open paren u circ v close paren times x ?

Since v(x) = 1/x, substitute 1/x into u: (u ∘ v)(x) = -2(1/x)² + 3 = 3 - 2/x², with x ≠ 0. For every allowed x, 2/x² is positive, so the output is always less than 3. As x approaches 0, the output decreases without bound, and it approaches 3 without ever reaching it. Thus the range is negative infinity to 3, not including 3: choice C.

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