(L-3)Let f ( x ) = 30 − 2 x − x 3 , then find the number of positive integral values of x which satisfies f ( f ( f ( x ))) f ( f ( − x )) .

Question

(L-3)Let f ( x ) = 30 − 2 x − x 3 , then find the number of positive integral values of x which satisfies f ( f ( f ( x ))) > f ( f ( − x )) .

TestHub · Accepted Answer

f ′ ( x ) = − 2 − 3 x 2 < 0 ⇒ f ( x ) is decreasing ∴ f ( f ( x )) < f ( x ) ⇒ f ( x ) > − x ⇒ 30 − x − x 3 > 0 ⇒ x 3 + x − 30 < 0 ⇒ ( x + 3 ) ( x 2 + 3 x + 16 ) < 0 ⇒ x < 3 ∴ N o . o f v a l u es = 2

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