Explicație pas cu pas:
[tex]f(x) = x - 1[/tex]
a)
[tex]f(0) = 0 - 1 = - 1[/tex]
[tex]f(1) = 1 - 1 = 0[/tex]
[tex]f(x) + f(x) = - 1 + 0 = - 1[/tex]
b)
intersecția cu axa Ox:
[tex]y = 0 = > f(x) = 0 \\ x - 1 = 0 = > x = 1 \\ = > A\left(1 ; 0\right)[/tex]
intersecția cu axa Oy:
[tex]x = 0 = > f(0) = - 1 \\ = > B\left(0 ;-1 \right)[/tex]
C este mijlocul segmentului AB:
[tex]C(x_{C} ;y_{C}) = > \\ x_{C} = \frac{x_{A} + x_{B}}{2} = \frac{1 + 0}{2} = \frac{1}{2} \\ y_{C} = \frac{y_{A} + y_{B}}{2} = \frac{0 + ( - 1)}{2} = - \frac{1}{2} \\ C \left( \frac{1}{2} ; - \frac{1}{2} \right)[/tex]
Aria OBC:
[tex]\left|\begin{array}{ccc}0&0&1\\0&-1&1\\ \frac{1}{2} & - \frac{1}{2} &1\end{array}\right| = \frac{1}{2} \\ [/tex]
[tex]Aria_{(OBC)} = \frac{1}{2}. | \frac{1}{2} | = \frac{1}{4} \\ [/tex]
sau:
[tex]Aria_{(OBC)} = \frac{1}{2}\cdot Aria_{(ABC)} = \frac{1}{2}\cdot\frac{ |OA\cdot OB| }{2} \\ = \frac{1}{2}\cdot \frac{ |1( - 1)| }{2} = \frac{1}{4} \\ [/tex]
