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Question: Answered & Verified by Expert
Let $f(x)=x^{12}-x^{9}+x^{4}-x+1$. Which of the following is true?
MathematicsQuadratic EquationKVPYKVPY 2011 (SB/SX)
Options:
  • A $\mathrm{f}$ is one-one
  • B $\mathrm{f}$ has a real root
  • C $\mathrm{f}^{\prime}$ never vanishes.
  • D f takes only positive values
Solution:
2098 Upvotes 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

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