Răspuns:
1.
[tex]f(x) = g(x) \\ 2x - 1 = {x}^{2} - 2x + 3 \\ 2x - 1 - {x}^{2} + 2x - 3 = 0 \\ 4x - 4 - {x = 0}^{2} \\ {x}^{2} - 4x + 4 = 0 \\ (x - 2) ^{2} = 0 \\ = > x = 2 \\ f(2) = 2 \times 2 - 1 = 4 - 1 = 3 \\ g(2) = {2}^{2} - 2 \times 2 + 3 = 4 - 4 + 3 = 3 \\ avem \: A(2,3)[/tex]
2. Functia este tangenta la axa Ox daca delta = 0!
[tex]a = 1 \\ b = - 1 \\ c = m \\ d = ( - 1)^{2} - 4 \times 1 \times m = 1 - 4m \\ 1 - 4m = 0 = > m = \frac{ 1}{4} [/tex]
4.
[tex] {(x - 1)}^{2} + x - 7 < 0 \\ {x}^{2} - 2x + 1 + x - 7 < 0 \\ {x}^{2} - x - 6 < 0 \\ {x }^{2} + 2x - 3x - 6 < 0 \\ x(x + 2) - 3(x + 2) < 0 \\ (x + 2)(x - 3) < 0 \\ solutie = > x∈ ( - 2 \: , \: 3)[/tex]
5.
[tex]f(x) \geqslant - 1 \\ {x}^{2} - 4x + 3 \geqslant - 1 \\ {x}^{2} - 4x + 3 + 1 \geqslant 1 \\ {x}^{2} - 4x + 4 \geqslant 0 \\ {( x - 2)}^{2} \geqslant 0 \\ = > x \: ∈R[/tex]
[tex] 6. {(x + 1)}^{2} \times (x - 1) \geqslant 0 \\ x1 = - 1 \\ x2 = 1 \\ det. \: inervalele \: de \: verificare \: \\ folosind \: valorile \: critice \\ ( - ∞, - 1) \\ ( - 1,1) \\ (1,+ ∞) \\ aleg \: cate \: o \: valoare \\ x1 = - 2 \\ x2 = 0 \\ x3 = 2 \\ = > ( - ∞, - 1) \: nu \: este \: solutie \\ ( - 1,1) \: este \: solutie \\ (1, + ∞) \: este \: solutie \\ x∈( - 1, + ∞)[/tex]
