# math

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)