Question

Determinati Imf unde:
a) f:[-3,1) apartine R f(x)=|x-2|

Answer 1

$f:[-3,1) \rightarrow \mathbb_{R}, f(x) = |x-2|\\ \\x\in [-3,1) \\ \\-3\leq x\ \textless \ 1\Big|-2 \\ -5\leq x-2\ \textless \ -1\Big|^2 \\ \\ (-5)^2\leq (x-2)^2\ \textless \ (-1)^2 \\ \\ 25\leq (x-2)^2\ \textless \ 1 \quad (F) \\ \\ 1\ < \ (x-2)^2\leq25\quad (A) \\ \\ 1\ < \ (x-2)^2\leq 25\Big|\sqrt{\boxed{~}} \\ \\ \sqrt{1} \ < \ \sqrt{(x-2)^2}\leq \sqrt{25} \\ \\ 1\ < \ |x-2|\leq 5 \\ \\ 1\ < \ f(x) \leq 5 \\ \\ \Rightarrow \boxed{Im f = (1,5]}$