Question

f:R-{1}->R-{1/2}, f(x)=2x+1/1-x

Sa se arate ca functia este surjectiva

Answer 1

$\hbox{ Fie} \ y \in R / \{\frac{1}{2}}\} \\\\ f(x)=y \\\\\\ \frac{2x+1}{1-x}=y \\\\ 2x+1=y-yx\\\\ 2x+yx=y-1 \\\\ x(2+y)=y-1 \\\\ x= \frac{y-1}{2+y} \ \ \in \ \ R/ \{1\} \\\\ ==\ \textgreater \ \forall \ y \in R / \{\frac{1}{2}}\} \ \exists \ x \in R / \ \{1\} ===\ \textgreater \ \hbox{f surjectie }$