Answer:
Given: f(x) = x - 5, g(x) = x² + 3x - 2
1. (f + g) (x) = f(x) + g(x)
= (x - 5) + (x² + 3x - 2)
(f + g) (x) = x² + 4x - 7
2. (f - g) (x) = f(x) - g(x)
= (x - 5) - (x² + 3x - 2)
= x - 5 - x² - 3x + 2
(f - g) (x) = -x² - 2x - 3
3. (f • g) (x) = f(x) • g(x)
= (x - 5) • (x² + 3x - 2)
= x³ + 3x² - 2x - 5x² - 15x + 10
(f • g) (x) = x³ - 2x² - 17x + 10
4. (g/f) (x) = g(x)/f(x)
(g/f) (x) = (x² + 3x - 2)/(x - 5)
5. (fog) (x) = f(g(x))
= (x² + 3x - 2) - 5
(fog) (x) = x² + 3x - 7
6. (gof) (x) = g(f(x))
= (x - 5)² + 3 (x - 5) - 2
= x² - 10x + 25 + 3x - 15 - 2
(gof) (x) = x² - 7x + 8
