Question

Determinati x € R pentru care au sens a) √2x-6 b) log3(x^2-9) ​

Answer 1

$\it\sqrt{2x-6}\ \Rightarrow 2x-6\geq0 \Rightarrow 2x\geq6|_{:2} \Rightarrow x\geq3 \Rightarrow x\in[3,\ \infty)\\ \\ log_3(x^2-9) \Rightarrow x^2-9>0 \Rightarrow x^2>9 \Rightarrow \sqrt{x^2}>\sqrt9 \Rightarrow \\ \\ \Rightarrow |x|>3 \Rightarrow x\in\mathbb{R}\setminus[-3,\ 3]$