Easy If you avoid the SILLIES

Number Theory Level 2

Let $f(x) = |x-2|$ and $g(x) = \underbrace{f(f(f(f....(f(x))))....)}_{n\text{ times}}$ . If the equation $g(x) = k , k\in (0,2)$ has $32$ distinct solutions then the value of $n$ is equal to :

The answer is 16.

1 solution

Suhas Sheikh
Jun 10, 2018

Easy enough Just plot f(X) And f(f(X)) You'll observe that the if no.of iterations of the function f(X) are n Then we have 2n distinct solutions for a k between (0,2) Hence 2n=32 Gives n=16

Easy If you avoid the SILLIES

The answer is 16.

1 solution

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