Resoluções de Análise Matemática, Demidovitch Cap. I Ex.20

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20. $y=arcsen \left( lg\frac{x}{10} \right);$

Resolução:

$|lg\frac{x}{10}| \le 1$ $\Longrightarrow$
$\left\{ \begin{array}{rll} lg\frac{x}{10} \le 1, & \hbox{se} & lg\frac{x}{10} \ge 0, x \gt 0 \\ -lg\frac{x}{10} \le 1, & \hbox{se} & lg\frac{x}{10} \lt 0, x \gt 0 \end{array}\right.$
$\Longrightarrow$ $\left\{ \begin{array}{rll} \frac{x}{10} \le 10, & \hbox{se} & \frac{x}{10} \ge 1, x \gt 0 \\ \frac{x}{10} \ge 10^{-1}, & \hbox{se} & \frac{x}{10} \lt 1, x \gt 0 \end{array}\right.$
$\Longrightarrow$ $\left\{ \begin{array}{rll} x \le 100, & \hbox{se} & x \ge 10, x \gt 0 \\ x \ge 1, & \hbox{se} & x \lt 10, x \gt 0 \end{array}\right.$

Entretanto, $D_y=x:x\in [1 ; 100]$