Asosiy tarkibga o'tish

1.1-bo'lim : Funktsiyalar

1-4-masalalar uchun berilgan funktsiyalar ko'rsatilgan funktsiyalarni baholashni amalga oshiradi.

  1. \(f\left( x \right) = 3 - 5x - 2{x^2} \) Yechim
    1. \(f\left( 4 \right) \)
    2. \(f\left( 0 \right)\)
    3. \(f\left( { - 3} \right) \)
    1. \(f\left( {6 - t} \right) \)
    2. \(f\left( {7 - 4x} \right)\)
    3. \(f\left( {x + h} \right) \)
  2. \(\displaystyle g\left( t \right) = \frac{t}{{2t + 6}} \) Yechim
    1. \(g\left( 0 \right) \)
    2. \(g\left( { - 3} \right)\)
    3. \(g\left( {10} \right) \)
    1. \(g\left( {{x^2}} \right) \)
    2. \(g\left( {t + h} \right)\)
    3. \(g\left( {{t^2} - 3t + 1} \right) \)
  3. \(h\left( z \right) = \sqrt {1 - {z^2}} \) Yechim
    1. \(h\left( 0 \right) \)
    2. \(h\left( { - \frac{1}{2}} \right)\)
    3. \(h\left( {\frac{1}{2}} \right) \)
    1. \(h\left( {9z} \right) \)
    2. \(h\left( {{z^2} - 2z} \right) \)
    3. \(h\left( {z + k} \right) \)
  4. \(\displaystyle R\left( x \right) = \sqrt {3 + x} - \frac{4}{{x + 1}} \) Yechim
    1. \(R\left( 0 \right) \)
    2. \(R\left( 6 \right)\)
    3. \(R\left( { - 9} \right) \)
    1. \(R\left( {x + 1} \right)\)
    2. \(R\left( {{x^4} - 3} \right)\)
    3. \(R\left( {\frac{1}{x} - 1} \right) \)

The farq koeffitsienti \(f\left( x \right) \) funksiyasi quyidagicha aniqlanadi:

\[\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}\]

5 – 9 masalalar uchun berilgan funksiyaning ayirma qismini hisoblang.

  1. \(f\left( x \right) = 4x - 9 \) Yechim
  2. \(g\left( x \right) = 6 - {x^2} \) Yechim
  3. \(f\left( t \right) = 2{t^2} - 3t + 9 \) Yechim
  4. \(\displaystyle y\left( z \right) = \frac{1}{{z + 2}} \) Yechim
  5. \(\displaystyle A\left( t \right) = \frac{{2t}}{{3 - t}} \) Yechim

10 – 17 masalalar uchun berilgan funksiyaning barcha ildizlarini aniqlang.

  1. \(f\left( x \right) = {x^5} - 4{x^4} - 32{x^3} \) Yechim
  2. \(R\left( y \right) = 12{y^2} + 11y - 5 \) Yechim
  3. \(h\left( t \right) = 18 - 3t - 2{t^2} \) Yechim
  4. \(g\left( x \right) = {x^3} + 7{x^2} - x \) Yechim
  5. \(W\left( x \right) = {x^4} + 6{x^2} - 27 \) Yechim
  6. \(f\left( t \right) = {t^{\frac{5}{3}}} - 7{t^{\frac{4}{3}}} - 8t \) Yechim
  7. \(\displaystyle h\left( z \right) = \frac{z}{{z - 5}} - \frac{4}{{z - 8}} \) Yechim
  8. \(\displaystyle g\left( w \right) = \frac{{2w}}{{w + 1}} + \frac{{w - 4}}{{2w - 3}} \) Yechim

18 – 22 masalalar uchun berilgan funksiyaning sohasi va diapazonini toping.

  1. \(Y\left( t \right) = 3{t^2} - 2t + 1 \) Yechim
  2. \(g\left( z \right) = - {z^2} - 4z + 7 \) Yechim
  3. \(f\left( z \right) = 2 + \sqrt {{z^2} + 1} \) Yechim
  4. \(h\left( y \right) = - 3\sqrt {14 + 3y} \) Yechim
  5. \(M\left( x \right) = 5 - \left| {x + 8} \right| \) Yechim

23 – 32 masalalar uchun berilgan funksiyaning sohasini toping.

  1. \(\displaystyle f\left( w \right) = \frac{{{w^3} - 3w + 1}}{{12w - 7}} \) Yechim
  2. \(\displaystyle R\left( z \right) = \frac{5}{{{z^3} + 10{z^2} + 9z}} \) Yechim
  3. \(\displaystyle g\left( t \right) = \frac{{6t - {t^3}}}{{7 - t - 4{t^2}}} \) Yechim
  4. \(g\left( x \right) = \sqrt {25 - {x^2}} \) Yechim
  5. \(h\left( x \right) = \sqrt {{x^4} - {x^3} - 20{x^2}} \) Yechim
  6. \(\displaystyle P\left( t \right) = \frac{{5t + 1}}{{\sqrt {{t^3} - {t^2} - 8t} }} \) Yechim
  7. \(f\left( z \right) = \sqrt {z - 1} + \sqrt {z + 6} \) Yechim
  8. \(\displaystyle h\left( y \right) = \sqrt {2y + 9} - \frac{1}{{\sqrt {2 - y} }} \) Yechim
  9. \(\displaystyle A\left( x \right) = \frac{4}{{x - 9}} - \sqrt {{x^2} - 36} \) Yechim
  10. \(Q\left( y \right) = \sqrt {{y^2} + 1} - \sqrt[3]{{1 - y}} \) Yechim

33-36-masalalar uchun berilgan funksiyalar juftligi uchun \(\left( {f \circ g} \right)\left( x \right) \) va \(\left( {g \circ f} \right)\left( x \right) \) ni hisoblang.

  1. \(f\left( x \right) = 4x - 1 \), \(g\left( x \right) = \sqrt {6 + 7x} \) Yechim
  2. \(f\left( x \right) = 5x + 2 \), \(g\left( x \right) = {x^2} - 14x \) Yechim
  3. \(f\left( x \right) = {x^2} - 2x + 1 \), \(g\left( x \right) = 8 - 3{x^2} \) Yechim
  4. \(f\left( x \right) = {x^2} + 3 \), \(g\left( x \right) = \sqrt {5 + {x^2}} \) Yechim