Question

Domeniul de definitie al funtiei f(x)= radical din xpatrat -5x+4

Answer 1

[tex]f(x)= \sqrt{x^2 -5x+4}\\ C.E.\:x^2 -5x+4 \geq 0\Leftrightarrow x^2-x-4x+4 \geq0 \Leftrightarrow x(x-1)-4(x-1) \geq 0\\ \Leftrightarrow(x-1)(x-4) \geq 0\\ (x-1)(x-4)=0\Leftrightarrow(x=1\:sau\:x=4)\\ daca\:facem\:tabelul,\:observam\:ca\:functia\:este\:pozitiva\:pe \:intervalul\\ (-\infty,1]\cup[4,\infty)\:si\:negativa\:pe\:intervalul\:(1,4).\\ Deci,f:(-\infty,1]\cup[4,\infty)\longrightarrow\mathbb{R}[/tex]