Verified answer

Смотри.....................

[tex]\displaystyle\bf\\\Big(\frac{1}{3} \Big)^{x^{2} -4x+3} \geq 3^{1-x} \\\\\\\Big(\frac{1}{3} \Big)^{x^{2} -4x+3} \geq \Big(\frac{1}{3} \Big)^{x-1} \\\\\\0 < \frac{1}{3} < 1 \ \ \ \Rightarrow \ \ \ x^{2} -4x+3\leq x-1\\\\\\x^{2} -4x+3-x+1\leq 0\\\\\\x^{2} -5x+4\leq 0\\\\\\(x-1)(x-4)\leq 0\\\\\\+ + + + + [1] - - - - - [4] + + + + +[/tex]

                 ////////////////////

[tex]\displaystyle\bf\\Otvet \ : \ x\in\Big[1 \ ; \ 4\Big][/tex]