MATHEMATICS ASSIGNMENTS (Coursework Sample)

Assignment 2 Given that f(x) = 2x2-x-3 and g(x) = 2x-6, to find the following combinations. Question 1 A (f+g)(x) = f(x) + g(x) Substitute the equation in the above expression. (f+g)(x) = 2x2-x-3 + (2x-6) (f+g)(x) = 2x2-x-3 + 2x-6 (f+g)(x) = 2x2-x-9 B (f-g)(x) = f(x) - g(x) Substitute the equation in the above expression. (f-g)(x) = 2x2-x-3 - (2x-6) (f-g)(x) = 2x2-x-3 - 2x+6 Collect the like term (f-g)(x) = 2x2-x-2x-3+6 (f-g)(x) = 2x2-3x+3 C (g-f)(x) = g(x) – f(x) Substitute the equation in the above expression. (g-f)(x) = 2x-6-(2x2-x-3) (g-f)(x) = 2x-6-2x2+x+3 Collect the like term and rearrange the equation (g-f)(x) = -2x2+2x+x-6+3 (g-f)(x) = -2x2+3x-3 D (g-f)(-2) = -2x2+3x-3 (g-f)(-2) = -2(-2)2+3(-2)-3 (g-f)(-2) = -8-6-3 (g-f)(-2) = -17 E (fg)(x) = (f(x)*g(x)) (fg)(x) = (2x2-x-3)(2x-6) (fg)(x) = 4x3-12x2-2x2+6x-6x+18 Collect the like terms (fg)(x) = 4x3-14x2+0+18 (fg)(2) = 4(2)3-14(2)2+18 (fg)(2) = 32-56+18 (fg)(2) = -6 F fgx= f(x)g(x)=2x2-x-32x-6 fgx= f(x)g(x)=2xx+1-3(x+1)2x-6 fgx= f(x)g(x)=(2x-3)(x+1)2(x-3) To calculate the domain of fgx= f(x)g(x) use the denominator 2x-6 2x-6=0 2x=6 X=3 fgx= f(x)g(x)=(2(3)-3)(3+1)2(3-3) fgx= f(x)g(x)=(3)(4)2(3-3)=120=∞(undefined) 2 Use f(x) = 2x+5 and g(x) = x2+x-6 to find the following combinations. A (f+g)(x) = f(x) + g(x) (f+g)(x) = 2x+5+ (x2+x-6) (f+g)(x) = 2x+5+ x2+x-6 Collect the like terms (f+g)(x) = x2+3x-1 B (g-f)(x) = g(x) -f(x) (g-f)(x) = x2+x-6 –(2x+5) (g-f)(x) = x2+x-6 –2x-5 (g-f)(x) = x2-x-11 C (g+f)(3) = g(x) + f(x) (g+f)(3) = x2+x-6 + (2x+5) (g+f)(3) = x2+x-6 +2x+5 (g+f)(3) = x2+3x-1 (g+f)(3) = (3)2+3(3)-1 (g+f)(3) = 9+9-1= 17 (g+f)(3) = 17 D (fg)(0) = f(x)*g(x) (fg)(0) = (2x+5)(x2+x-6) (fg)(0) = 2x3+2x2-12x+5x2+5x-30 Collect the like term (fg)(0) = 2x3+7x2-7x-30 (fg)(0) = 2(0)2+7(0)2-7(0)-30 (fg)(0) = 0+0+0-30 (fg)(0) = -30 E Use the function in D to solve E problem (fg)(-1) = 2x3+7x2-7x-30 (fg)(-1) = 2(-1)3+7(-1)2-7(-1)-30 (fg)(-1) = -2+7+7-30 (fg)(-1) = -18 F gf1=g(x)f(x) gf1= x2+x-62x+5=(1)2+1-621+5=-47 gf1= -47 G fg-3=f(x)g(x) fg-3= 2x+5x2+x-6=2(-3)+5(-3)2+(-3)-6=-6+59-3-6 fg-3=-10=∞(undefined) 3 A Given f(x) = 2x-3 and g(x) = 5x+4;to use the composite (f•g)(x) = f(g(x)) in the following composites. Substitute g(x) into f(x) Therefore: (f•g)(x) = 2(5x+4)-3 (f•g)(x) = 10x+8-3 (f•g)(x) = 10x+5 B (g•f)(x) = g(f(x)) (g•f)(x) = 5(2x-3) +4 (g•f)(x) = 10x-15 +4 (g•f)(x) = 10x-11 C For this composite function (f•g)(-3) ,use the solution in 3(A ) Part. Therefore; (f•g)(x) = 10x+5 (f•g)(-3) = 10(-3)+5 (f•g)(-3) = -30+5 (f•g)(-3) = -25 4 Given the following function; f(x) = x2-8x-9 g(x) = x2+6x+5 Use the following composite function (f•g)(x) = f(g(x)) (f•g)(x) = (x2+6x+5)2-8(x2+6x+5)-9 Expand this expression; (x2+6x+5)2 = (x2+6x+5) (x2+6x+5) = x4+6x3+5x2+6x3+36x2+30x+5x2+30x+25 Collect the like term = x4+12x3+46x2+60x+25 ………1 For this expression open the bracket -8(x2+6x+5) = -8x2-48x-40 ,,,,,,,,,,,,,,2 Combine the expression 1 and 2 (f•g)(x) = x4+12x3+46x2+60x+25--8x2-48x-40-9 (f•g)(x) = x4+12x3+38x2+12x-24 Use this composite to solve the following problems. A (f•g)(0) = x4+12x3+38x2+12x-24 (f•g)(0) = (0)4+12(0)3+38(0)2+12(0)-24 (f•g)(0) = 0+0+0+0-24 (f•g)(0) = -24 B (f•g)(1) = x4+12x3+38x2+12x-24 (f•g)(1) = (1)4+12(1)3+38(1)2+12(1)-24 (f•g)(1) = 1+12+38+12-24 (f•g)(1) = 39 C Find the following composite; (g•f)(x)= g(f(x)) (g•f)(x)= (x2-8x-9)2+6(x2-8x-9) Expand this expression; (x2-8x-9)2 = (x2-8x-9) (x2-8x-9) = x4-8x3-9x2-8x3+64x2+72x-9x2+72x+81 = x4-16x3+46x2+144x+81………..1 Open the bracket of this expression 6(x2-8x-9) = 6x...