P2 36

INTEGER ANS TYPE

1) Let f(x) = 30 - 2x - x³ , then find the number of positive integral values of x which satisfies f ( f ( f ( x ) ) ) > f ( f ( -x ) ) .

5 Answers

x Îµ (-âˆž,3)

Integer ans type

Ans is 2

U're right eureka

Post u're method plzzz

341

Hari Shankar ·2010-02-16 20:01:15

Denote the composition fofofo..f(x) n times by fⁿ(x)

f(x) is monotonically decreasing.

Hence

f^3(x)>f^2(-x) \Rightarrow f^2(x)<f(-x) \Rightarrow f(x)>-x

\Rightarrow x^3+3x-30 which is valid only for x=1,2 among +ve integers

Thanks Sir

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