Question

Se considera functia f:[0, 1)-R, f(x)=-x la a 2, sa se determine multimea valorilor functiei f

Answer 1

$f:[0,1) \to \mathbb{R}, ~~f(x) = -x^2. \\ \\ x\in [0,1) \Rightarrow \underset{\text{Putem ridica la p\u{a}trat deoarece capetele inegalitatii nu sunt negative}}{\underbrace{0\leq x < 1\Big|^2}} \Rightarrow \\ \\ \Rightarrow 0^2 \leq x^2< 1^1 \Rightarrow 0 \leq x^2<1\Big|\cdot (-1) \Rightarrow (-1)\cdot 0 \geq -x^2 > -1 \Rightarrow \\ \\ \Rightarrow 0\geq -x^2 > -1 \Rightarrow -1 < -x^2 \leq 0 \Rightarrow -x^2 \in (-1,0] \Rightarrow \\ \\ \Rightarrow \boxed{f(x) \in (-1,0]}$