a) 5x / 3 + ( 4 - x) / 2 = ( x+2)/4 -1
multiplying entire equation by 12
20x + 6 ( 4 - x) = 3 (x+2) - 12
20x + 24 - 6x = 3x + 6 - 12
20x - 6x - 3x = - 24 + 6 - 12
x = - 30/11
b) -11 < 5/9 F - 32 < 17
adding 32 on all sides
- 11 + 32 < 5/9 F < 17 + 32
21 < 5/9 F < 49
multiplying all sides by 9/5
189/ 5 < F < 441 / 5
c) 8 - 10x = 5x^2
5x^2 + 10x - 8 = 0
x = [ - 10 +- sqrt ( 100 + 160) ] / 10
x = -1 + sqrt 65 / 5 , -1 - sqrt 65 / 5
12. Consider the polynomial function f(x) = xº - xé - 10x - 8 a) Solve the equation algebraically f(x) = 0 by factoring. b) Sketch the graph of f(x) without a calculator. Justify your steps. c) Complete the table: (3 marks) (2 marks) (2 marks) y intercept x intercepts end behaviour degree
Find the inverse, f-1(x), for each function 7. f(x) x3 2х+3 8. f (x) 5x4
Solve each inequality and graph its solution. 11) -12+ 3(-4 + 10x)2 3(1+ 10x)+5 12) 9-10k- 5k+ 62 5(9- 11k)+10(-7+4k) -10-8 -6 6 -5-43 -2 -1 01234 13) -5 +ks7 14) -4n> 8 4 2 0 2 468 10 12 14 7-6-5-4-3-2-1 01234 5 6 15) 6x+4 <4 16) 10p-9 s61 8 -7-6-4 -3-210 123 17) 3+-8x- 10 S-23 18) 4v-3-7>-26 6-5432-01234S 7-6-5432101 234
solve for x: 9^( 4x-8 )=〖9 〗^(10x+2 )
Factor the polynomial f(x). Then solve the equation f) o. 10) f(x) x3+5x2- 9x-45 State the domain of the rational function. (6 points) 11) g(x) =ー2 x +2 Given that the polynomial function has the given zero, find the other zeros. 12) f(x)=x3-4x2 + 9x-10:2
18. Solve by completing the square: a. x² - 10x = -8 b. 3x² +6x = 72
Detrmine the limit for each of the following problems 2x2 + 10x b) (2x – 1)(3 – x) lim x= (x - 1)(x + 3) c) lim X-5 X-5 5x4 + 8x2 a) lim x+0 3x4 – 16x2 1 - cos(x) d) lim X5 x2
34. Solve the following matrix equations. 32. -8 -2 -62 X = -50 2 -8 -6 -30 22 - IHAR -8 -4 -8 33. १० X + H - -36 30 143 -150 0 -12 11 -6 10 34. -34 -88-38 22 20 -29 -111 35. -[B1- 8 36.8 SHAILE-AGH)-[2]
3. |(6x2/3 + 2 cos x – 5) dx 4. Find f(x) given that f'(x) = 5x4 – 3x2 + 2 and f(1) = 4.
#35,37 In Exercises 21 through 38, differentiate the given function and simplify your answer 21. f(x) (2x 3)14 22. fx) 23. f(x) = (2x + 1)4 24. f(x) = V 5x6-12 25. fx)-(a 4r3 78 26. ft) (3r 729)5 27, f(t) = V5 3x 28. f(x)=- (6x2 +5x+ 1)2 5rt_ V4x2 30. 4x +1 31. f(x)=: (1-x2)4 2 3(5x4 1)2 32. f(x) = (1-x2)4 (135) f(x) = (x + 2)3(2x-1)5 36. f(x) 2(3x 1)(5x 3)2 (1 -x 1 - 5x2...