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i’ll give u 30 points and mark u the brainliest if u answer some/all of it thank youu :)

IV. Let fx= x2+6, gx= -x+7, hx= x2-9x+14, and jx= 6x3+5x2-4x+3.
Find the following: (Show complete solutions; 2 points each)

Ill Give U 30 Points And Mark U The Brainliest If U Answer Someall Of It Thank Youu IV Let Fx X26 Gx X7 Hx X29x14 And Jx 6x35x24x3 Find The Following Show Compl class=

Sagot :

FIND THE FOLLOWING:

Let:

  • f(x) = x² + 6
  • g(x) = -x + 7
  • h(x) = x² - 9x + 14
  • j(x) = 6x³ + 5x² - 4x + 3.

19.) (j + f)(x) = j(x) + f(x)

  • (j + f)(x) = (6x³ + 5x² - 4x + 3) + (x² + 6)

  • (j + f)(x) = 6x³ + 5x² - 4x + 3 + x² + 6

  • (j + f)(x) = 6x³ + 5x² + x² - 4x + 3 + 6

  • (j + f)(x) = 6x³ + 6x² - 4x + 9

20.) [tex](\frac{h}{g})[/tex] (x) = [tex](\frac{h(x)}{g(x)})[/tex]

  • = [tex]\frac{x² - 9x + 14}{-x + 7}[/tex]

  • = -x + 2

21.) (h o g)(x) = h(g(x))

  • (h o g)(x) = (-x + 7)² - 9(-x + 7) + 14

  • (h o g)(x) = x² - 14x + 49 + 9x - 63 + 14

  • (h o g)(x) = x² - 14x + 9x + 49 - 63 + 14

  • (h o g)(x) = x² - 5x

22.) (g o f)(x) = g(f(x))

  • (g o f)(x) = -(x² + 6) + 7

  • (g o f)(x) = -x² - 6 + 7

  • (g o f)(x) = -x² + 1

23.) (f o g)(x) = f(g(x))

  • (f o g)(x) = (-x + 7)² + 6

  • (f o g)(x) = x² - 14x + 49 + 6

  • (f o g)(x) = x² - 14x + 55

24.) (h o f)(2) = h(f(2))

  • (h o f)(2) = (2² + 6)² - 9(2² + 6) + 14

  • (h o f)(2) = (4 + 6)² - 9(4 + 6) + 14

  • (h o f)(2) = 10² - 9(10) + 14

  • (h o f)(2) = 100 - 90 + 14

  • (h o f)(2) = 10 + 14

  • (h o f)(2) = 24

25.) (j o g)(1) = j(g(1))

  • (j o g)(1) = 6(-1 + 7)³ + 5(-1 + 7)² - 4(-1 + 7) + 3

  • (j o g)(1) = 6(216) + 5(36) + 4 - 28 + 3

  • (j o g)(1) = 1,296 + 180 + 4 - 28 + 3

  • (j o g)(1) = 1,476 - 21

  • (j o g)(1) = 1,455

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