Think Again, Please

Algebra Level 3

\[\large\begin{align} f(x) = &x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}} + \dfrac{1}{x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}}}\\&+\dfrac{1}{x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}} + \dfrac{1}{x^2 + \dfrac{1}{x^2} + \dfrac{1}{x^2 + \dfrac{1}{x^2}}}} \end{align} \]

What is the smallest real value that the function \( f \) can attain over all real values of \( x ?\)

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