3.4-bo'lim: Funktsiyaning ta'rifi

1-3-masalalar uchun berilgan munosabat funksiya ekanligini aniqlang.

1. \(\left\{ {\left( {2,4} \right),\left( {3, - 7} \right),\left( {6,10} \right)} \right\}\) Yechim
2. \(\left\{ {\left( { - 1,8} \right),\left( {4, - 7} \right),\left( { - 1,6} \right),\left( {0,0} \right)} \right\}\) Yechim
3. \(\left\{ {\left( {2,1} \right),\left( {9,10} \right),\left( { - 4,10} \right),\left( { - 8,1} \right)} \right\}\) Yechim

4-6-masalalar uchun berilgan tenglama funksiya ekanligini aniqlang.

1. \(\displaystyle y = 14 - \frac{1}{3}x\) Yechim
2. \(y = \sqrt {3{x^2} + 1} \) Yechim
3. \({y^4} - {x^2} = 16\) Yechim
4. \(f\left( x \right) = 3 - 2{x^2}\) berilgan bo'lib, quyidagi har birini aniqlang.
   1. \(f\left( 0 \right)\)
   2. \(f\left( 2 \right)\)
   3. \(f\left( { - 4} \right)\)
   4. \(f\left( {3t} \right)\)
   5. \(f\left( {x + 2} \right)\)
   Yechim
5. Berilgan \(\displaystyle g\left( w \right) = \frac{4}{{w + 1}}\) quyidagilardan har birini aniqlang.
   1. \(g\left( { - 6} \right)\)
   2. \(g\left( { - 2} \right)\)
   3. \(g\left( 0 \right)\)
   4. \(g\left( {t - 1} \right)\)
   5. \(g\left( {4w + 3} \right)\)
   Yechim
6. Berilgan \(h\left( t \right) = {t^2} + 6\) quyidagilardan har birini aniqlang.
   1. \(h\left( 0 \right)\)
   2. \(h\left( { - 2} \right)\)
   3. \(h\left( 2 \right)\)
   4. \(h\left( {\sqrt x } \right)\)
   5. \(h\left( {3 - t} \right)\)
   Yechim
7. \(h\left( z \right) = \left\{ {\begin{array}{*{20}{l}}{3z}&{{\rm{if }}z < 2}\\{1 + {z^2}}&{{\rm{if }}z \ge 2}\end{array}} \right.\) berilgan bo'lib, quyidagi har birini aniqlang.
   1. \(h\left( 0 \right)\)
   2. \(h\left( 2 \right)\)
   3. \(h\left( 7 \right)\)
   Yechim
8. \(f\left( x \right) = \left\{ {\begin{array}{*{20}{l}}6&{{\rm{if }}x \ge 9}\\{x + 9}&{{\rm{if }}2 < x < 9}\\{{x^2}}&{{\rm{if }}x \le 2}\end{array}} \right.\) berilgan bo'lib, quyidagilardan har birini aniqlang.
   1. \(f\left( { - 4} \right)\)
   2. \(f\left( 2 \right)\)
   3. \(f\left( 6 \right)\)
   4. \(f\left( 9 \right)\)
   5. \(f\left( {12} \right)\)
   Yechim

12 va 13-masalalar uchun berilgan funksiya uchun ayirma qismini hisoblang. \(f\left( x \right)\) funksiyasi uchun farq koeffitsienti quyidagicha aniqlanadi:

1. \(f\left( x \right) = 4 - 9x\) Yechim
2. \(f\left( x \right) = 2{x^2} - x\) Yechim

14-18-masalalar uchun funksiya sohasini aniqlang.

1. \(A\left( x \right) = 6x + 14\) Yechim
2. \(\displaystyle f\left( x \right) = \frac{1}{{{x^2} - 25}}\) Yechim
3. \(\displaystyle g\left( t \right) = \frac{{8t - 24}}{{{t^2} - 7t - 18}}\) Yechim
4. \(g\left( w \right) = \sqrt {9w + 7} \) Yechim
5. \(\displaystyle f\left( x \right) = \frac{1}{{\sqrt {{x^2} - 8x + 15} }}\) Yechim