# Solution to Mathematical Problems Involving Functions (Essay Sample)

Solving of mathematics problem

source..Student’s Name

Professor’s Name

Subject

Date

Task 3

1

f(x) = 2x^2 - x - 3

g(x) = 2x - 6

A

(f + g)(x) = (2x^2 - x - 3) + (2x - 6) = 2x^2 + x - 9

B

(f - g)(x) = (2x^2 - x - 3) - (2x - 6) = 2x^2 - 3x + 3

C

(g - f)(x) = (2x - 6) - (2x^2 - x - 3) = -2x^2 + 3x - 3

D

(g - f)(-2) = -2 ×( - 2)^2 + 3 × (- 2) - 3 = - 17

E

(fg)(x) = (2x^2 - x - 3) × (2x - 6)

(fg)(2) = (2×(2)^2 - 2 - 3) × (2(2) - 6) = - 6

F

(f / g)(x) = (2x^2 - x - 3) / (2x - 6) = (2x^2 - 3x + 2x - 3) / (2x - 6)

(f / g)(x) = (2x - 3)(x + 1) / (2x - 6)

G

(f / g)(2) = (2(2) - 3)(2 + 1) / (2(2) - 6) = - 1.5

Domain : R - {1.5}

2

f(x) = 2x + 5

g(x) = x^2 + x - 6

A

(f + g)(x) = (2x + 5) + (x^2 + x - 6) = x^2 + 3x - 1

B

(g - f)(x) = (x^2 + x - 6) - (2x + 5) = x^2 - x - 11

C

(g + f)(x) = (x^2 + x - 6) + (2x + 5) = x^2 + 3x - 1

(g + f)(3) = (3^2 + 3 - 6) + (2(3) + 5) = 3^2 + 3(3) - 1 = 17

D

(fg)(0) = (2(0) + 5) × (0^2 + 0 - 6) = - 30

E

(fg)(-1) = (2(- 1) + 5) × (- 1^2 + (- 1) - 6) = - 18

F

(g / f)(1) = (1^2 + 1 - 6) / (2(1) + 5) = - 0.571

G

(f / g)(-3) = (2(- 3)+ 5) / ((- 3)^2 + (-3) - 6) = Not defined

3

f(x) = 2x – 3

g(x) = 5x + 4

(f º g)(x) = f(g(x))

A

(f º g)(x) = 2( 5x + 4) - 3 = 10x + 5

B

(g º f)(x) = 5( 2x - 3) + 4 = 10x - 11

C

(f º g)(-3) = 10 × (- 3) + 5 = -25

4

f(x) = x^2 – 8x - 9

g(x) = x^2 + 6x + 5

(f º g)(x) = f(g(x)) = (x^2 + 6x + 5)^2 - 8(x^2 + 6x + 5) - 9

A

(f º g)(0) = (0^2 + 6(0) + 5)^2 - 8(0^2 + 6(0) + 5) - 9 = -24

B

(f º g)(1)

### Other Topics:

- The Difference between Hearing Culture and Deaf CultureDescription: Communication plays a significant role in modern society. Hearing and deaf cultures are two distinct facets, which use different means of communicating. According to Hill (163), there are at least two deaf individuals in every one thousand people. Continuous learning is the cornerstone to understanding every community or cultural group. ...1 page/≈275 words| 4 Sources | MLA | Literature & Language | Essay |
- Being Enlightened about EnlightenmentDescription: Enlightenment is argued as a process by which the goals of education are realized. This definition acknowledges the reality that the human in his or her natural state is deprived of certain levels of knowledge. Enlightenment is defined as the effort of one to think for him or herself. Teachers and ...4 pages/≈1100 words| 2 Sources | MLA | Literature & Language | Essay |
- Analyzing Susan Farrell's "Fight vs. Flight"Description: The chosen text for the essay is a peer-reviewed article by Susan Farrell titled Fight vs. Flight A Reevaluation of the Dee in Alice Walker’s “Everybody’s use”. According to Farrell’s work, Mother’s narrative provides a skewed and false portrayal of Dee’s character. She believes that Mother’s envy of Dee...2 pages/≈550 words| 2 Sources | MLA | Literature & Language | Essay |