Question Number 54278 by ajfour last updated on 01/Feb/19
$${If}\:{f}\:{be}\:{n}\rightarrow{n}\:\:\:\left({n}\in\mathbb{N}\right)\:{and}\:{is}\:{increasing}, \\ $$$${f}\left({f}\left({n}\right)\right)=\mathrm{3}{n};\:{find}\:{f}\left(\mathrm{2}\right). \\ $$$${options}:\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\mathrm{4}\:. \\ $$
Commented by mr W last updated on 02/Feb/19
$${if}\:{f}\left({f}\left({x}\right)\right)=\mathrm{3}{x} \\ $$$$\Rightarrow{f}\left({x}\right)=\sqrt{\mathrm{3}}{x}\:? \\ $$
Commented by ajfour last updated on 02/Feb/19
$${f}\left(\mathrm{2}\right)=?,\:{we}\:{have}\:{to}\:{choose}\:{among} \\ $$$$\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\:\:{Sir}. \\ $$
Commented by mr W last updated on 02/Feb/19
$${i}\:{know}.\:{if}\:{f}\left({x}\right)\:{is}\:{a}\:{continous}\:{function}, \\ $$$${it}\:{could}\:{be}\:{f}\left({x}\right)=\sqrt{\mathrm{3}}{x}\:{to}\:{fulfill}\:{f}\left({f}\left({x}\right)\right)=\mathrm{3}{x}. \\ $$$${but}\:{here}\:{n}\in{N},\:{f}\left({n}\right)\:{in}\:{not}\:{continuous}, \\ $$$${but}\:{must}\:{be}\:{increasing}.\:{you}\:{can}\:{try} \\ $$$${and}\:{see}\:{the}\:{only}\:{possibility}\:{for}\:{f}\left(\mathrm{2}\right) \\ $$$${is}\:{f}\left(\mathrm{2}\right)=\mathrm{3}\:{to}\:{keep}\:{f}\left({f}\left({n}\right)\right)=\mathrm{3}{n}. \\ $$
Commented by ajfour last updated on 02/Feb/19
$${i}\:{shall}\:{ask}\:{the}\:{answer}\:{n}\:{let}\:{you} \\ $$$${know}\:{soon}\:{Sir}.\left({from}\:{my}\:{nephew}\right). \\ $$