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Pages:
8 pages/≈2200 words
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Subject:
Communications & Media
Type:
Exam
Language:
English (U.S.)
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Topic:

math

Instructions:
Math Essay: Mathematics is generally defined as the science that deals with numbers. It involves operations among numbers, and it also helps you to calculate the product price, how many discounted prizes here, and If you good in maths so you can calculate very fast. Mathematicians and scientists rely on mathematics principles in their real-life to experiments with new things every day. Many students say that ” I hate mathematics ” and maths is a useless subject, but it is wrong because without mathematics your life is tough to survive. Math has its applications in every field.
Content:

Abdullah Khan

Teacher name

Class number

Aug 25, 2022

Mathematics & Statistics Problem Solution

1. Use f(x) = 2x2 – x – 3 and g(x) = 2x – 6 for following combinations

A.(f + g) (x)

= f (x) + g (x)

= (2x2 – x – 3) + (2 x – 6)

= 2x2 – x – 3 + 2x – 6

= 2x2 – x + 2x – 3 – 6

= 2x2 + x -9

B. (f – g) (x)

= f (x) – g (x)

= (2x2 – x –3) – (2x – 6)

= 2x2 – x – 3 – 2x + 6

= 2x2 – x – 2x– 3 + 6

= 2x2 – 3x + 3

C.(g – f) (x)

= g (x) – f (x)

= (2x – 6) – (2x2 – x – 3)

= 2x – 6 – 2 x2 + x +3

= – 2x2 + x + 2x + 3 – 6

= –2x2 + 3x – 3

D.(g – f) (–2)

= g (–2) – f (–2)

= [2(–2) – 6] – [2(–2)2 – (–2) – 3]

= [– 4– 6] – [8+2–3]

= –10–8–2+3

= -17

E. (fg) (2)

= f (2) * g (2)

= [2(2) – 6] * [2(2)2 – (2) – 3]

= [4– 6] * [8–2–3]

= [–2] * [3]

= – 6

F. (f / g) (x)

= f(x) / g(x)

= (2x2 – x – 3) / (2x – 6)

= (2x – 3) (x + 1) / (2x – 6)

Domain of (f / g) (x) is (– ∞, 3) ꓴ (3, ∞)

2. Use f(x) = 2x + 5 and g(x) = x2 + x – 6 for following combinations.

A. (f + g) (x)

= f (x) + g (x)

= (2x + 5) + (x2 + x – 6)

= 2x + 5 + x2 + x – 6

= x2 + 2x + x + 5– 6

= x2 + 3x – 1

B.(g – f) (x)

= g (x) – f (x)

= (x2 + x – 6) – (2x + 5)

= x2 + x – 6 – 2x – 5

= x2 – 2x + x – 5– 6

= x2 – x – 11

C. (g + f) (3)

= g (3) + f (3)

= (32 + 3 – 6) + (2(3) + 5)

= (9 + 3 – 6) + (6 + 5)

= 6 + 11

= 17

D.(fg) (0)

= f (0) * g (0)

= (2(0) + 5) * (02 + (0) – 6)

= (0+5) * (0 + 0 – 6)

= 5 *(– 6)

= – 30

E.(fg) (–1)

= f (–1) * g (–1)

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