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

JEE MATHEMATICS MCQ: FUNCTIONS

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The largest interval for which

{x^{12}} - {x^9} + {x^4} - x + 1 > 0\;

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Correct option: D

0 < x < \infty

The correct answer is D. The inequality holds for all x > 0. By considering different intervals, we can prove that the expression is always positive.

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}