The largest interval containing x for which x | vedclass

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(C) Let $f(x) = x^{12} - x^9 + x^4 - x + 1$. We analyze the expression by grouping terms: $f(x) = x^9(x^3 - 1) + x(x^3 - 1) + 1$. Alternatively,consid

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$-\infty < x < \infty$

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(C) Let $f(x) = x^{12} - x^9 + x^4 - x + 1$. We analyze the expression by grouping terms: $f(x) = x^9(x^3 - 1) + x(x^3 - 1) + 1$. Alternatively,consider the expression as $f(x) = x^{12} - x^9 + x^4 - x + 1$. If $x \ge 1$,then $x^9(x^3 - 1) \ge 0$ and $x(x^3 - 1) \ge 0$,so $f(x) \ge 1 > 0$. If $x \le 0$,then $f(x) = x^{12} + x^4 + (-x^9 - x) + 1$. Since $x \le 0$,$-x^9 \ge 0$ and $-x \ge 0$,so $f(x) > 0$. If $0  0$. Since $f(x) > 0$ for all real $x$,the largest interval is $(-\infty, \infty)$.

The largest interval containing $x$ for which $x^{12}-x^9+x^4-x+1 > 0$ is

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