Aufgaben zur Bestimmung von Definitionsmengen

1

Gib für folgende Funktionen die maximale Definitionsmenge an (G=R)\left(G=ℝ\right) .

  1. f(x)=4x32x5f(x)=\dfrac{4x-3}{2x-5}

  2. f(x)=3x3+7x22xf(x)=\dfrac{3x^3+7}{x^2-2x}

  3. f(x)=2x+x719x2+13x+14f\left(x\right)=\dfrac{2x+x^7}{\frac19x^2+\frac13x+\frac14}

  4. f(x)=2x4x20,01x21f\left(x\right)=\dfrac{2x^4-x^2}{0{,}01x^2-1}

  5. f(x)=7x+4f\left(x\right)=\sqrt{7x+4}

  6. f(x)=x25x+6f\left(x\right)=\sqrt{x^2-5x+6}

  7. f(x)=17x+5x3f(x)=\sqrt{17x}+5x-3

  8. f(x)=x24x+36f(x)=\sqrt[6]{x^2-4x+3}

  9. f(x)=ln(x5)f(x)=\ln(x-5)

  10. f(x)=ln(6xx29)f\left(x\right)=\ln\left(6x-x^2-9\right)

  11. f(x)=log6(x37x)f(x)=\mathrm{log}_6(x^3-7x)

  12. f(x)=5x  tan(x)f\left(x\right)=5x\;\tan\left(x\right)

  13. f(x)=7x2tan(2x)f\left(x\right)=7x^2\tan\left(2-x\right)

  14. f(x)=(x+5)  tan  (x212π)f\left(x\right)=\left(x+5\right)\;\tan\;\left(x^2-\frac12\pi\right)

  15. f(x)=1x2+6x+9f\left(x\right)=\dfrac1{\sqrt{x^2+6x+9}}

  16. f(x)=lg(x2x)x+2f\left(x\right)=\dfrac{\lg\left(x^2-x\right)}{\sqrt{x+2}}

  17. f(x)=1+3x+33x2sin(x)f\left(x\right)=\dfrac{1+3x+33x^2}{\sin\left(x\right)}

  18. f(x)=123451sin(x12π)f\left(x\right)=\dfrac{12345}{1-\sin\left(x-\frac12\pi\right)}

2

Gib für folgende Funktionen die maximale Definitionsmenge an (G=R)\left(G=ℝ\right) .

  1. f(x)=5x+170,64x2+1,12x+0,49f\left(x\right)=\dfrac{5x+17}{0{,}64x^2+1{,}12x+0{,}49}

  2. f(x)=x2+4x+42x2+20x+60f\left(x\right)=\dfrac{\sqrt{x^2+4x+4}}{\sqrt{2x^2+20x+60}}

  3. f(x)=(4x9)12188xf\left(x\right)=\dfrac{\left(4x-9\right)^\tfrac12}{18-8x}

  4. f(x)=6xx29f\left(x\right)=\sqrt{6x-x^2-9}

  5. f(x)=112x22f\left(x\right)=\dfrac1{\frac12x^2-2}

  6. f(x)=x3+x2+x+149x214f\left(x\right)=\dfrac{x^3+x^2+x+1}{\frac49x^2-\frac14}

  7. f(x)=sin(x)x24x+4f\left(x\right)=\dfrac{\sin(x)}{x^2-4x+4}

  8. f(x)=1x2+6x9f(x)=\dfrac1{-x^2+6x-9}

  9. f(x)=2ax+4bx2+8cx3805x2f\left(x\right)=\dfrac{2\mathrm{ax}+4\mathrm{bx}^2+8\mathrm{cx}^3}{80-5x^2}

  10. f(x)=(2x)x+x2+x3+x4x314xf\left(x\right)=\left(2-x\right)\cdot\dfrac{x+x^2+x^3+x^4}{x^3-\frac14x}

  11. f(x)=xsin(x)f\left(x\right)=\dfrac x{\sin(x)}

  12. f(x)=1234+5x+6x2cos(x+4)f\left(x\right)=123\cdot\dfrac{4+5x+6x^2}{\cos\left(x+4\right)}

  13. f(x)=67893  cos(x)sin(x)f\left(x\right)=\dfrac{6789}{\sqrt3\;\cos\left(x\right)-\sin\left(x\right)}

  14. f(x)=5x2a36x216xf(x)=\dfrac{5x^2-a}{36x^2-16x}

    strobl-f.de (Aufgabenstellung)
  15. f(x)=1x616x+1f(x)=\dfrac1{x-6}-\dfrac1{6x+1}

    strobl-f.de (Aufgabenstellung)

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