If the average of $x$ and $\frac{1}{x}(x \neq 0)$ is $M,$ then the average of $x^{2}$ and $\frac{1}{x^{2}}$ is

  • A

    $1-M^{2}$

  • B

    $1-2 M$

  • C

    $2 M ^{2}-1$

  • D

    $2 M ^{2}+1$

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