If f be n→n (n∈N) and is increasing, f(f(n))=3n; find f(2). options: 1, 2, 3,4 .


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Question Number 54278 by ajfour last updated on 01/Feb/19

$I f f b e n \to n (n \in N) a n d i s i n c r e a s i n g,$ $f (f (n)) = 3 n; f i n d f (2) .$ $o p t i o n s : 1, 2, 3, 4 .$
Commented by mr W last updated on 02/Feb/19

$i f f (f (x)) = 3 x$ $\Rightarrow f (x) = \sqrt{3} x ?$
Commented by ajfour last updated on 02/Feb/19

$f (2) = ?, w e h a v e t o c h o o s e a m o n g$ $1, 2, 3, 4 S i r .$
Commented by mr W last updated on 02/Feb/19

$i k n o w . i f f (x) i s a c o n t i n o u s f u n c t i o n,$ $i t c o u l d b e f (x) = \sqrt{3} x t o f u l f i l l f (f (x)) = 3 x .$ $b u t h e r e n \in N, f (n) i n n o t c o n t i n u o u s,$ $b u t m u s t b e i n c r e a s i n g . y o u c a n t r y$ $a n d s e e t h e o n l y p o s s i b i l i t y f o r f (2)$ $i s f (2) = 3 t o k e e p f (f (n)) = 3 n .$
Commented by ajfour last updated on 02/Feb/19

$i s h a l l a s k t h e a n s w e r n l e t y o u$ $k n o w s o o n S i r . (f r o m m y n e p h e w) .$
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