Grupa I Zadanie 1 [latex]f(x)=frac{x+2}{3x+1}\ D_f={x in mathbb{R}: 3x+1 ot=0}=mathbb{R} ackslash{-frac{1}{3}}\ g(x)=sqrt{x-2}\ D_g={x in mathbb{R}: x-2 geq0}={x in mathbb{R}: xgeq 2}= extless 2;infty)\ [/latex] Zadanie 2 w załączniku Zadanie 3 Wykres w załączniku. [latex]f(x)=frac{1}{2}x-3\ D=mathbb{R}\ Zw=mathbb{R}\ x_0=6 in D,bo quad f(6)=0\ y_0=-3,bo quad f(0)=-3\ f uparrow dla x in mathbb{R}\[/latex] Zadanie 4 [latex]f(x)=(m-3)x-2\ f uparrow Leftrightarrow m-3 extgreater 0\ m-3 extgreater 0\ m extgreater 3\ m in (3; infty)[/latex] Grupa II Zadanie 1 [latex]g(x)=frac{x^2+1}{2x-1}\ D_g={x in mathbb{R}: 2x-1 ot=0}=mathbb{R} ackslash {frac{1}{2}}\ h(x)=sqrt{5-x}\ D_h={x in mathbb{R}: 5-x geq0}=(-infty;5 extgreater \ f(x)=frac{x^2+2x+7}{x^2-9}\ D_f={x in mathbb{R}: x^2-9 ot=0}={x in mathbb{R}: x^2 ot=9}=mathbb{R}ackslash{-3;3}\[/latex] [latex]p(x)=frac{sqrt{7-x}}{x(x+4)}\ D_p={x in mathbb{R}: 7-xgeq 0 wedge x(x+4) ot=0}=(-infty;7 extgreater cap (mathbb{R} ackslash{0;-4})=\ =(-infty;-4) cup (-4;0) cup (0;7 extgreater [/latex] Zadanie 2 w załączniku Zadanie 3 Wykres w załączniku. [latex]f(x)=-3x-1\ D=mathbb{R}\ Zw=mathbb{R}\ x_0=frac{-1}{3} in D,bo quad f(frac{-1}{3})=0\ y_0=-1,bo quad f(0)=-1\ f downarrow dla x in mathbb{R}\[/latex] Zadanie 4 [latex]f(x)=(frac{2}{5}-m)x+3\ f downarrow Leftrightarrow frac{2}{5}-m extless 0\ frac{2}{5}-m extless 0\ m extgreater frac{2}{5}\ min (frac{2}{5}; infty)[/latex]
