Matematik opg 921 922 928


Opg. 921

  1. LaTex: (f+g)(x)=f(x)
    • LaTex: -3x+1=0
    • LaTex: x=\frac{1}{3}
  2. LaTex: 5x+4=19
    • LaTex: x=3
  3. LaTex: (2x+5)\times(-3x+1)=10
    • LaTex: -6x^2-13x-5=0
    • LaTex: x=\frac{13\pm\sqrt{-13^2-4\times -6\times -5}}{2\times -6} = -3,5 = 1\frac{1}{3}
  4. LaTex: 3(-3x+1)=21
    • LaTex: -9x+3=21
    • LaTex: x=\frac{18}{-9}=-2
  5. LaTex: \frac{2x+5}{-3x+1}=1
    • LaTex: 2x+5=-3x+1
    • LaTex: 5x=-4
    • LaTex: x=\frac{-4}{5}=-0,8
  6. LaTex: \frac{-3x+1}{2x+5}=1
    • LaTex: -3x+1=2x+5
    • LaTex: -5x=+4
    • LaTex: x=\frac{4}{-5}=-0,8

Opg. 922

LaTex: \begin{array}{l} (f + g)(x) = 2x - 1 + x^2 \\ (f - g)(x) = 2x + 7 - x^2 \\ (f \times g)(x) = 2x^3 - 12 \\ \left( {\frac{f}{g}} \right)(x) = \frac{{2x + 3}}{{x^2 - 4}} \\ \left( {\frac{g}{f}} \right)(x) = \frac{{x^2 - 4}}{{2x + 3}} \\ \end{array}

LaTex: \begin{array}{l} (f + g)(3) = 2 \times 3 - 1 + 3^2 = 14 \\ (f - g)(3) = 2 \times 3 + 7 - 3^2 = 4 \\ (f \times g)(3) = 2 times 3^3 - 12 = 6 \\ \left( {\frac{f}{g}} \right)(3) = \frac{{2 \times 3 + 3}}{{3^2 - 4}} = 1.8 \\ \left( {\frac{g}{f}} \right)(3) = \frac{{3^2 - 4}}{{2 \times 3 + 3}} = 0.556 \\ \end{array}

Opg. 928

F1
(Lige)
  • 1²+1 = -1²+1 = 2
F2
(ingenting)
  • 1³+1 != -1³+1
F3
(Lige)
  • 1²+1^4 = -1²+-1^4 = 2
F4
(Ulige)
  • 1^3+1=-(-1^3-1)=2
F5
F6
(Lige)
  • 4=4
F7
(Ingenting)
  • LaTex: \frac{1-3}{1+4}\not=\frac{-1-3}{-1+4}
F8
(Lige)
  • LaTex: \frac{1^2-4}{1^4+3}=\frac{-1^2-4}{-1^4+3}=-0,75
F9
(Ingenting)
  • LaTex: \frac{1^3-1}{1^2+5}\not=\frac{-1^3--1}{-1^2+5}
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