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# MATHEMATICS ASSIGNMENTS (Coursework Sample)

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THIS IS MATHEMATICS ASSIGNMENTS THAT COVERED SERIES OF TOPICS SUCH AS ALGEBRA AND COMPOSITE FUNCTION.AND COMPREHENSIVE SOLUTIONS WAS PROVIDED FOR ALL THE SOLUTIONS AND MLA STYLES WAS USED TO WRITE THE ENTIRE SOLUTIONS.
THE FOLLOWING TOPICS WAS COVERED ,THEY ARE: 1. COMPOSITE FUNCTION 2. MEASURATION WHICH COVERED AREA OF RECTANGLE 3. WORD LEADING PROBLEM. source..

Content:

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...

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