Given \( x_0 \neq 0 \), if the iteration formula \( x_{n+1} = \frac{1}{2}\left( -\frac{7}{x_n} + x_n \right) \), \( n \geq 0 \) is used to find the root of \( f(x) = 0 \), then \( f(x) = \)
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This formula matches Newton-Raphson iteration \( x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} \) for finding purely imaginary roots, or a rearranged fixed-point iteration format \( x = g(x) \) designed to isolate roots where \( x^2 = -7 \).