Let $f (x) = 1 - x - x^{3}$ Then the real values of $x$ satisfying the inequality $1 - f (x) - f^{3} (x) > f (1 - 5 x)$ are

(- 2, 0)

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(0, 2)

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(2, \infty)

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(- \infty, - 2)

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Solution

The correct options are
A $(- 2, 0)$
C $(2, \infty)$
$f (x) = 1 - x - x^{3}$

Replacing $x$ by $f (x), f (f (x)) = 1 - f (x) - f^{3} (x)$

Hence, the given equation is

$f (f (x)) > f (1 - 5 x), f (x) < 1 - 5 x$

$f (x) = 1 - x - x^{3}$

$1 - x - x^{3} < 1 - 5 x$

$x^{3} - 4 x > 0$

$x (x - 2) (x + 2) > 0$

So, $x \in (- 2, 0) \cup (2, \infty)$

Suggest Corrections

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