Side 1 av 1
vgs kos 2
Lagt inn: 16/12-2016 12:31
av Janhaa
Hvis [tex]\,\,f(x)=\frac{x}{x-1}[/tex],
bestem så:
[tex](fofof...of)_{9\,\text ganger}[/tex]
der
[tex]fof = f(f(x))[/tex]
Re: vgs kos 2
Lagt inn: 16/12-2016 12:46
av Drezky
[tex]fof=f(f(x))=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-1}=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-\frac{x+1}{x-1}}=\frac{\frac{x}{x-1}}{\frac{x-x+1}{x-1}}=\frac{x}{x-1}*\frac{x-1}{1}=\frac{x}{1}=x[/tex]
[tex]fofof=f(f(f(x)))=\frac{x}{x-1}[/tex]
[tex]fofofof=f(f(f(f)))=\frac{\frac{x}{x-1}}{\frac{1}{x-1}}=\frac{x}{x-1}*\frac{x-1}{1}=\frac{x}{1}=x[/tex]
Ser et mønster..
[tex]fofofofof=\frac{x}{x-1}[/tex]
[tex]fofofofofofofofof=f(x)=\frac{x}{x-1}[/tex]
Re: vgs kos 2
Lagt inn: 16/12-2016 13:32
av Janhaa
Drezky skrev:[tex]fof=f(f(x))=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-1}=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-\frac{x+1}{x-1}}=\frac{\frac{x}{x-1}}{\frac{x-x+1}{x-1}}=\frac{x}{x-1}*\frac{x-1}{1}=\frac{x}{1}=x[/tex]
[tex]fofof=f(f(f(x)))=\frac{x}{x-1}[/tex]
[tex]fofofof=f(f(f(f)))=\frac{\frac{x}{x-1}}{\frac{1}{x-1}}=\frac{x}{x-1}*\frac{x-1}{1}=\frac{x}{1}=x[/tex]
Ser et mønster..
[tex]fofofofof=\frac{x}{x-1}[/tex]
[tex]fofofofofofofofof=f(x)=\frac{x}{x-1}[/tex]
Bra, stemmer.