1c)
[tex]\it f(x) \geq0 \Leftrightarrow 3x-2\geq 0 \Leftrightarrow 3x\geq2 \Leftrightarrow x\geq\dfrac{2}{3} \Leftrightarrow x \in\left [\dfrac{2}{3},\ \ \infty\right) [/tex]
1d)
[tex]\it f:\mathbb{R} \longrightarrow \mathbb{R} , \ f(x) = 3x-2
\\\;\\ \\\;\\
d)\ \ f(1) = 3\cdot1-2 = 3-2 = 1
\\\;\\
f(f(1)) = f(1) = 1[/tex]
4)
[tex]\it sin^245^o+cos^245^0 = 1\ (formula\ fundamental\u{\it a} \ a\ trigonometriei)[/tex]
3)
[tex]\it x \in (0^0, \ 90^0) \Longrightarrow sinx\ \textgreater \ 0,\ cosx\ \textgreater \ 0
\\\;\\
cosx = \sqrt{1-sin^2x} = \sqrt{1-\left(\dfrac{1}{3}\right)^2} = \sqrt{1-\dfrac{1}{9}} = \sqrt{\dfrac{9}{9}-\dfrac{1}{9}} =
\\\;\\ \\\;\\
= \sqrt{\dfrac{8}{9}} = \dfrac{\sqrt{4\cdot2}}{3} = \dfrac{2\sqrt2}{3}
[/tex]
2e)
[tex]\it f(x) \leq0 \Rightarrow x^2-5x+6 \leq0 \Rightarrow x^2-2x-3x+6\leq0 \Rightarrow
\\\;\\
\Rightarrow x(x-2) -3(x-2)\leq0 \Rightarrow (x-2)(x-3) \leq0 \Rightarrow x\in[2,\ 3][/tex]
(Am aplicat semnul funcției de gradul al II-lea).
