Answer:
1c 12
1d 4x - 3
2c 10x + 20
2d 60x² + 160x + 100
3c
Domain is -3 ≤ x ≤ 3
Range is -2 ≤ g(x) ≤ 2
Step-by-step explanation:
Question 1 : f(x) = 2x - 3
- 1c. 3 - f(-3)
f(-3) = 2(-3) - 3 = -6 - 3 = -9
3 - f(-3) = 3 - (-9) = 12
- 1d. f(2x)
f(2x) = 2(2x) - 3 = 4x - 3
Question 2: f(x) = 8x + 10, g(x) = 2x
- 2c: 2f(x) - 3g(x)
2f(x) - 3g(x) = 2(8x + 10) - 3(2x) = 16x + 20 - 6x = 10x + 20
- 2d : (f(x))² - (g(x))²
f(x)² - g(x)² = ( f(x) + g(x) ) . (f(x) - g(x)).
This uses the fact that a² - b² = (a+b)(a-b)
f(x) + g(x) = 8x + 10 + 2x = 10x + 10
f(x) - g(x) = 8x + 10 - 2x = 6x + 10
f(x)² - g(x)² = (10x + 10) . (6x + 10)
Apply FOIL method: (a + b)(c + d) = ab + bc +cd + bd
(10x + 10) x (6x + 10) = (10x)(6x) + (10x)(10) + (10)(6x) + (10)(10)
= 60x² + 100x + 60x + 100
= 60x² + 160x + 100
