1. f(x) = 3x + 5, g(x) = x² - 4
(f + g)(x) = 3x + 5 + x² - 4 = x² + 3x + 1
2. f(x) = 3x + 5, g(x) = x² - 4
(f - g)(x) = 3x + 5 - (x² - 4) = -x² + 3x + 9
3. f(x) = 3x + 5, g(x) = x² - 4
(f · g)(x) = (3x + 5)(x² - 4) = 3x³ - 12x + 5x² - 20 = 3x³ + 5x² - 12x - 20
4. f(x) = 3x + 5, g(x) = x² - 4
(f / g)(x) = (3x + 5)/(x² - 4), x ≠ ±2
5. f(x) = x² - 3x + 7, g(x) = 2x - 5
(f + g)(x) = x² - 3x + 7 + 2x - 5 = x² - x + 2
6. f(x) = x² - 3x + 7, g(x) = 2x - 5
(f - g)(x) = x² - 3x + 7 - (2x - 5) = x² - 5x + 12
7. f(x) = x² - 3x + 7, g(x) = 2x - 5
(f · g)(x) = (x² - 3x + 7)(2x - 5) = 2x³ - 5x² - 6x² + 15x + 14x - 35 = 2x³ - 11x² + 29x - 35
8. f(x) = x² - 3x + 7, g(x) = 2x - 5
(f / g)(x) = (x² - 3x + 7)/(2x - 5), x ≠ 5/2
9. f(x) = 3x² - 2x + 1, g(x) = 4x - 3
(f + g)(x) = 3x² - 2x + 1 + 4x - 3 = 3x² + 2x - 2
10. f(x) = 3x² - 2x + 1, g(x) = 4x - 3
(f - g)(x) = 3x² - 2x + 1 - (4x - 3) = 3x² - 6x + 4
11. f(x) = 3x² - 2x + 1, g(x) = 4x - 3
(f · g)(x) = (3x² - 2x + 1)(4x - 3) = 12x³ - 9x² - 8x² + 6x + 4x - 3 = 12x³ - 17x² + 10x - 3
12. f(x) = 3x² - 2x + 1, g(x) = 4x - 3
(f / g)(x) = (3x² - 2x + 1)/(4x - 3), x ≠ 3/4
13. f(x) = x² - 3x + 2, g(x) = x - 1
(f + g)(x) = x² - 3x + 2 + x - 1 = x² - 2x + 1
14. f(x) = x² - 3x + 2, g(x) = x - 1
(f - g)(x) = x² - 3x + 2 - (x - 1) = x² - 4x + 3
15. f(x) = x² - 3x + 2, g(x) = x - 1
(f · g)(x) = (x² - 3x + 2)(x - 1) = x³ - x² - 3x² + 3x + 2x - 2 = x³ - 4x² + 5x - 2
16. f(x) = x² - 3x + 2, g(x) = x - 1
(f / g)(x) = (x² - 3x + 2)/(x - 1) = ((x-1)(x-2))/(x-1) = x - 2, x ≠ 1
17. f(x) = 2x² - 5x + 3, g(x) = x - 3
(f + g)(x) = 2x² - 5x + 3 + x - 3 = 2x² - 4x
18. f(x) = 2x² - 5x + 3, g(x) = x - 3
(f - g)(x) = 2x² - 5x + 3 - (x - 3) = 2x² - 6x + 6
19. f(x) = 2x² - 5x + 3, g(x) = x - 3
(f · g)(x) = (2x² - 5x + 3)(x - 3) = 2x³ - 6x² - 5x² + 15x + 3x - 9 = 2x³ - 11x² + 18x - 9
20. f(x) = 2x² - 5x + 3, g(x) = x - 3
(f / g)(x) = (2x² - 5x + 3)/(x - 3) = ((2x-3)(x-1))/(x-3), x ≠ 3
Parent Tip: Review the logic above to help your child master the concept of composition of functions worksheet with answers.
