Fonksiyon

Question

1)$f(x)=\frac{x-1}{x}$ olduguna gore f(2x-1) in f(x) cinsinden Degeri ?

2)F:R---->R

$f(x)=3^{x-1}$

O.g f(m+n+2) esiti ?

3)$f(x)=2^x+2^{-x}$ o.g f(2x) in f(x) cinsinden esiti ?

Lutfen anlasilir anlatin.

Answer 1

$f(x)=\frac{x-1}{x}=1-\frac{1}{x} \\ \frac{1}{x}=1-f(x) \\ x=\frac{1}{1-f(x)} (*)\\ 2x-1=\frac{1}{1-f(2x-1)} \\ 2x=\frac{1}{1-f(2x-1)}+1=\frac{2-f(2x-1)}{1-f(2x-1)} \\ x=\frac{2-f(2x-1)}{2(1-f(2x-1))} (-)\\ (*) \text{ ve }(-)\text{'den} \\ \frac{1}{1-f(x)}=\frac{2-f(2x-1)}{2-2f(2x-1)} \\ f(2x-1)=\frac{2f(x)}{1+f(x)}$

Comments

Daha pratik bir yolu yokmi cok uzun geldi