[tex]1)~-5(x+2)\ \textless \ 25 \Leftrightarrow~x+2\ \textgreater \ -5 \Leftrightarrowx\ \textgreater \ -7. \\ Solutie:~\boxed{x \in(-7;+\infty)}. \\ \\ 2)~A(1;1) \in G_{f}\Rightarrow f(1)=1 \Leftrightarrow a+b=1. \\ ~~~~B(-1;3)\in G_{f} \Rightarrow f(-1)=3 \Leftrightarrow -a+b=3. \\ \\ \left \{ {{a+b=1} \atop {-a+b=3}} \right.\Leftrightarrow \left \{ {{a+b=1} \atop {2b=4}} \right.\Leftrightarrow \left \{ {{a=1-b} \atop {b=2}} \right. \Leftrightarrow \left \{ {{a=-1} \atop {b=2}} \right. . \\ Deci~\boxed{f(x)=-x+2}.[/tex]
[tex]3)~1- \frac{3x+4}{5}=2 ~~~~~~~|*5 \\ 5-(3x+4)=10 \\ 5-3x-4=10 \\ 1-3x=10 \\ -3x=9 \\ \boxed{x=-3}[/tex]
[tex]4)~ \left \{ {{2x+y=1} \atop {x-y=-4}} \right. \Leftrightarrow \left \{ {{3x=-3} \atop {x-y=-4}} \right. \Leftrightarrow \left \{ {{x=-1} \atop {y=x+4}} \right. \Leftrightarrow \left \{ {{x=-1} \atop {y=3}} \right. . \\ Solutie:(x,y)=(-1;3).[/tex]
[tex]5)~A( \frac{a-5}{2};2a-7) \in G_{f} \Rightarrow f( \frac{a-5}{2})=2a-7 \Leftrightarrow -2* \frac{a-5}{2}+3=2a-7 \\ \Leftrightarrow -a+5+3=2a-7 \Leftrightarrow 15=3a \Rightarrow \boxed{a=5}.[/tex]
[tex]6)~ 2x^{2} +7x-4=0 \\ \Delta= b^{2} -4ac=49-4*(-4)*2=81. \\ \\ x_{1}= \frac{-b+ \sqrt{\Delta} }{2a}= \frac{-7+9}{4}= \frac{1}{2}. \\ x_{2}= \frac{-b- \sqrt{\Delta} }{2a}= \frac{-7-9}{4}=-4. \\ \Solutie:~\boxed{x\in\{ \frac{1}{2};-4\}}. [/tex]
