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Let $f(x)=x^{12}-x^{9}+x^{4}-x+1$. Which of the following is true?
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Verified Answer
The correct answer is:
f takes only positive values
$\begin{aligned} f(x) &=x^{9}\left(x^{3}-1\right)+x\left(x^{3}-1\right)+1 \text { positive for } x \geq 1 \text { or } x \leq 0 \\ &=1-x+x^{4}-x^{9}+x^{12} \text { positive for } x \in(0,1) \end{aligned}$
$\mathrm{f}(\mathrm{x})$ is always positive
$\mathrm{f}(\mathrm{x})$ is always positive
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