Think Again, Please

Algebra Level 3

f(x)=x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2+1x2\large\begin{aligned} 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{aligned}

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

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