Question

Dominio de F (x) = Pi/2 - 2arcsen(x-1)

Answer 1

$\large\begin{array}{l} \textsf{Encontrar o dom\'inio da fun\c{c}\~ao}\\\\ \mathsf{f(x)=\dfrac{\,\pi\,}{2}-2\,arcsen(x-1)} \end{array}$


$\large\begin{array}{l} \textsf{Restri\c{c}\~oes para o dom\'inio:}\\\\ \textsf{O argumento da fun\c{c}\~ao arcsen deve estar no intervalo}\\ \mathsf{[-1,\,1],}\textsf{ ou seja}\\\\ \mathsf{-1\le x-1\le 1}\\\\ \mathsf{-1+1\le x-1+1\le 1+1}\\\\ \mathsf{0\le x\le 2} \end{array}$


$\large\begin{array}{l} \textsf{Portanto, o dom\'inio de f \'e}\\\\ \mathsf{Dom(f)=\{x\in\mathbb{R}:~0\le x\le 2\}}\\\\\\ \textsf{ou usando a nota\c{c}\~ao de intervalos,}\\\\ \mathsf{Dom(f)=[0,\,2].} \end{array}$


$\large\begin{array}{l} \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$