wyznacz dziedzinę funkcji : g(x) = log₄ 3-x / x h (x) = log (x² +3x -4 )

[latex]g(x) = log_4 frac{3-x}{x}[/latex] 1. [latex]x eq 0[/latex] 2. [latex]frac{3-x}{x}>0[/latex] [latex](3-x)x>0[/latex] [latex]-x(x-3)>0 /:(-1)[/latex] [latex]x(x-3)<0[/latex] Parabola z ramionami skierowanymi do góry [latex]x in left( 0;3 ight)[/latex] Z 1 i 2 [latex]x in left( 0;3 ight)[/latex] ===================== [latex]h (x) = log (x^2 +3x -4 ) [/latex] [latex]x^2 +3x -4> 0[/latex] [latex]Delta=3^2-4 cdot 1 cdot (-4)=9+16=25[/latex] [latex]sqrt{Delta}= sqrt{25}=5 [/latex] [latex]x_1= frac{-3-5}{2} = frac{-8}{2}=-4 [/latex] [latex]x_2= frac{-3+5}{2} = frac{2}{2}=1[/latex] Parabola z ramionami skierowanymi do góry [latex]x in left(- infty ;-4 ight) cup left( 1;+ infty ight) [/latex]