Question

afla f(x) cand f(x)-2f(4-2x/x+2)=1 afla f(x), x diferit de -2

Answer 1

[tex]f(x)-2f(\frac{4-2x}{x+2})=1\\ x\rightarrow \frac{4-2x}{x+2}\\ f(\frac{4-2x}{x+2})-2f(x)=1\\ \text{Scadem cele doua relatii}\\ 3f(x)-3f(\frac{4-2x}{x+2})=0\ |:3\\ f(x)-f(\frac{4-2x}{x+2})=0\\ f(x)=f(\frac{4-2x}{x+2})\\ \text{ Inlocuim in prima relatie }\\ f(x)-2f(x)=1 \Rightarrow -f(x)=1\Rightarrow f(x)=-1[/tex]
Deci f este functia constanta -1