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(C) Given $f(x) = \left[2\left(1 - \frac{x^{25}}{2}\right)\left(2 + x^{25}\right)\right]^{\frac{1}{50}}$.Simplifying the expression inside the bracket

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$2$

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(C) Given $f(x) = \left[2\left(1 - \frac{x^{25}}{2}\right)\left(2 + x^{25}\right)\right]^{\frac{1}{50}}$.Simplifying the expression inside the bracket:$f(x) = \left[\left(2 - x^{25}\right)\left(2 + x^{25}\right)\right]^{\frac{1}{50}} = \left(4 - x^{50}\right)^{\frac{1}{50}}$.Now,calculate $f(f(x))$:$f(f(x)) = \left(4 - (f(x))^{50}\right)^{\frac{1}{50}} = \left(4 - (4 - x^{50})\right)^{\frac{1}{50}} = (x^{50})^{\frac{1}{50}} = x$.Since $f(f(x)) = x$,it follows that $f(f(f(x))) = f(x)$.Given $g(x) = f(f(f(x))) + f(f(x))$,we substitute the results:$g(x) = f(x) + x$.For $x = 1$:$g(1) = f(1) + 1 = (4 - 1^{50})^{\frac{1}{50}} + 1 = 3^{\frac{1}{50}} + 1$.Since $1 Therefore,the greatest integer less than or equal to $g(1)$ is $\lfloor 3^{\frac{1}{50}} + 1 \rfloor = 2$.

Let $f: R \rightarrow R$ be a function defined by $f(x) = \left(2\left(1 - \frac{x^{25}}{2}\right)\left(2 + x^{25}\right)\right)^{\frac{1}{50}}$. If the function $g(x) = f(f(f(x))) + f(f(x))$,then the greatest integer less than or equal to $g(1)$ is

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