Kopertina e librit Matematika 10-11 (fletore pune)

Zgjidhja e ushtrimit 5

Zgjidhja e ushtrimit 5 të mësimit 6.2 - Funksionet në librin Matematika 10-11 (fletore pune) nga shtëpia botuese Botime Pegi me autorë Clare Pass.

Pyetja

Janë dhënë funksionet f(x)=2x−8f(x)=2x-8 dhe g(x)=1x+4g(x)=\dfrac{1}{x+4}. Gjeni:

  1. f(0)f(0)
  2. g(0)g(0)
  3. f(1)f(1)
  4. g(1)g(1)
  5. f(−2)f(-2)
  6. g(−2)g(-2)
  7. f(12)f\Big(\dfrac{1}{2}\Big)
  8. g(12)g\Big(\dfrac{1}{2}\Big)
  9. f(−23)f\Big(\dfrac{-2}{3}\Big)
  10. g(−23)g\Big(\dfrac{-2}{3}\Big)
  11. f(x2)f(x^2)
  12. g(x2)g(x^2)
  13. f(g(x))f(g(x))
  14. g(f(x))g(f(x))
  15. f(g(1))f(g(1))
  16. g(f(1))g(f(1))
  17. f(g(−2))f(g(-2))
  18. g(f(−2))g(f(-2))

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Zgjidhja

  1. f(0)=(2×0)−8=0−8=−8f(0)= (2 \times 0) - 8 = 0-8 = -8
  2. g(0)=10+4=14g(0)=\dfrac{1}{0+4}=\dfrac{1}{4}
  3. f(1)=(2×1)−8=2−8=−6f(1) = (2 \times 1) - 8 = 2 - 8 = -6
  4. g(1)=11+4=15g(1) = \dfrac{1}{1+4}=\dfrac{1}{5}
  5. f(−2)=(2×(−2))−8=−4−8=−12f(-2) = (2 \times (-2))-8 = -4-8=-12
  6. g(−2)=1(−2)+4=12g(-2) = \dfrac{1}{(-2)+4}=\dfrac{1}{2}
  7. f(12)=(2×12)−8=1−8=−7f\Big(\dfrac{1}{2}\Big) = \Big(\cancel2 \times \dfrac{1}{\cancel2}\Big) - 8 = 1-8=-7
  8. g(12)=112+4=192=29g\Big(\dfrac{1}{2}\Big) = \dfrac{1}{\frac{1}{2}+4}=\dfrac{1}{\frac{9}{2}}=\dfrac{2}{9}
  9. f(−23)=(2×−23)−8=−43−8=−4−243=−283f\Big(\dfrac{-2}{3}\Big) = \Big(2 \times \dfrac{-2}{3}\Big)-8 = -\dfrac{4}{3}-8=\dfrac{-4-24}{3}=-\dfrac{28}{3}
  10. g(−23)=1−23+4=1103=310g\Big(\dfrac{-2}{3}\Big)=\dfrac{1}{-\frac{2}{3}+4}=\dfrac{1}{\frac{10}{3}}=\dfrac{3}{10}
  11. f(x2)=2x2−8f(x^2)=2x^2-8
  12. g(x2)=1x2+4g(x^2)=\dfrac{1}{x^2+4}
  13. f(g(x))=2×1x+4−8=2x+4−8f(g(x))=2 \times \dfrac{1}{x+4}-8 = \dfrac{2}{x+4}-8
  14. g(f(x))=12x−8+4=12x−4g(f(x))=\dfrac{1}{2x-8+4}=\dfrac{1}{2x-4}
  15. f(g(1))=21+4−8=25−8=2−405=−385f(g(1))=\dfrac{2}{1+4}-8 = \dfrac{2}{5}-8=\dfrac{2-40}{5}=-\dfrac{38}{5}
  16. g(f(1))=12−4=−12g(f(1))=\dfrac{1}{2-4}=-\dfrac{1}{2}
  17. f(g(−2))=2−2+4−8=22−8=1−8=−7f(g(-2))=\dfrac{2}{-2+4}-8=\dfrac{2}{2}-8=1-8=-7
  18. g(f(−2))=12(−2)−4=1−4−4=1−8=−18g(f(-2))=\dfrac{1}{2(-2)-4}=\dfrac{1}{-4-4}=\dfrac{1}{-8}=-\dfrac{1}{8}