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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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