Question

4. Se consideră funcţia f:R→R, f(x)= -x+2,x€(-inf. -1)
3,x€(-1,2)
X+1,X€ [2,inf.)

Să se calculeze f(-3), ƒ(1),
f(0), f(1), f(2), ƒ(3).

Answer 1

Explicație pas cu pas:

$f(x) = \begin{cases} -x+2, \ & \ x \in (- \infty; -1) \\ \ \ \ \ \ \ \ \ \ \ 3, \ & \ x \in (-1,2) \\ \ \ \ x + 1, \ & \ x \in [2,+\infty)\\ \end{cases}$

$- 3 < - 1 \implies f(x) = -(-3) + 2 = 3 + 2 = 5$

$- 1 < 1 < 2 \implies f(1) = 3$

$- 1 < 0 < 2 \implies f(0) = 3$

$- 1 < 1 < 2 \implies f(1) = 3$

$2 \leqslant 2 \implies f(2) = 2 + 1 = 3$

$2 \leqslant 3 \implies f(3) = 3 + 1 = 4$