Răspuns:
[tex](a) \boldsymbol{ \red{-2}}, \ (b) \boldsymbol{ \red{\dfrac{4\sqrt{5} }{5}}}[/tex]
Explicație pas cu pas:
f(x) = 2x + 4
[tex]a) \ f\bigg(-\dfrac{1}{2}\bigg) = 2\bigg(-\dfrac{1}{2}\bigg) + 4 = - 1 + 4 = 3[/tex]
[tex]f\bigg(\dfrac{1}{2}\bigg) = 2 \cdot \dfrac{1}{2} + 4 = 1 + 4 = 5[/tex]
[tex]f\bigg(-\dfrac{1}{2}\bigg) - f\bigg(\dfrac{1}{2}\bigg) = 3 - 5 = \bf- 2[/tex]
b) Intersecția cu axa Ox: y = 0 ⇒ f(x) = 0 ⇒ 2x + 4 = 0 ⇒ 2x = -4
[tex]x = -2 \implies A(-2, 0)[/tex]
Intersecția cu axa Oy: x = 0 ⇒ f(x) = 4 ⇒ B(0, 4)
OA = |-2 | = 2, OB = | 4 | = 4
[tex]AB = \sqrt{2^2 + 4^2} = \sqrt{20} = 2\sqrt{5}[/tex]
[tex]d(O, G_f) = \dfrac{OA \cdot OB}{AB} = \dfrac{2 \cdot 4}{2\sqrt{5} } = \bf\dfrac{4\sqrt{5} }{5}[/tex]
