The composite function of \( f_{1}\left(f_{2}\left(f_{3}\left(\ldots \ldots\left(f_{\mathrm{n}}(... VIDEO
The composite function of \( f_{1}\left(f_{2}\left(f_{3}\left(\ldots \ldots\left(f_{\mathrm{n}}(x)\right) \ldots.\right)\right.\right. \) is a decreasing function and \( r \) functions out of total \( n \) functions are decreasing functions while the rest are increasing. The maximum value of \( r(n-r) \) is
(a) \( \frac{n^{2}-4}{4} \) when \( n \) is of the form \( 4 k \)
(b) \( \frac{n^{2}}{4} \) whe \( n \) nis an even number
(c) \( \frac{n^{2}-1}{4} \) when \( n \) is an odd number
(d) \( \frac{n^{2}}{4} \) when \( n \) is of the form \( 4 k+2 \)
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