Question

41 o dominio da função f, definida por:

Answer 1

$\displaystyle \sf \frac{5\sqrt[6]{\sf x-2}}{(x-1)\cdot(x-2)\cdot(x-3)} \\\\\\ \underline{\text{numerador}} :\\\\ \sqrt[6]{\sf x-2} \to \geq 0 \to x-2\geq0 \to x\geq 2 \\\\ \underline{\text{denominador}}: \\\\ (x-1)\cdot(x-2)\cdot(x-3) \neq 0 \\\\ x-1\neq 0 \to x \neq 1\\\\ x-2\neq 0 \to x \neq 2 \\\\ x-3\neq 0 \to x \neq 3$

$\sf \underline{\text{fazendo a interse{\c c}{\~a}o com o intervalo do numerador, temos }}:\\\\ \ (x\geq 2) \ \cap \ (x\neq 1) \ \cap \ (x\neq 2) \ \cap \ (x\neq 3 ) \to x > 2 \ e \ x\neq 3 \\\\ \displaystyle \sf portanto : \\\\ \boxed{\sf D(f) = \{x\in\mathbb{R}\ | \ x > 2 \ e\ x \neq 3 \} }\checkmark$

letra c