Answer:
a) -4x + 4
b) 4x² - 6x - 10
c) 8
d) 8
Step-by-step explanation:
a) To find f + g, we add the two functions together.
So, (f + g)(x) = f(x) + g(x)
= (2x² - 5x - 3) + (-2x² + x + 7)
= 2x² - 5x - 3 - 2x² + x + 7
= -4x + 4
b) To find f - g, we subtract g from f.
So, (f - g)(x) = f(x) - g(x)
= (2x² - 5x - 3) - (-2x² + x + 7)
= 2x² - 5x - 3 + 2x² - x - 7
= 4x² - 6x - 10
c) To evaluate (f + g)(-1), we substitute -1 for x in the expression (f + g)(x).
(f + g)(-1) = -4(-1) + 4
= 4 + 4
= 8
d) To evaluate (2f - g)(3), we substitute 3 for x in the expression (2f - g)(x).
(2f - g)(3) = 2(2(3)² - 5(3) - 3) - (-2(3)² + 3 + 7)
= 2(18 - 15 - 3) - (-2(9) + 3 + 7)
= 2(0) - (-18 + 3 + 7)
= 0 - (-8)
= 0 + 8
= 8
