Answer:
A. (f + g)(3) = 29
B. (fg)(-1) = 18
Step-by-step explanation:
To find (f + g)(3), we need to add the two functions (f and g) and then evaluate the sum at x = 3.
Similarly, for (fg)(-1), we need to multiply the two functions and then evaluate the product at x = -1. Let's calculate both:
A. (f + g)(3):
[tex] (f + g)(x) = f(x) + g(x) [/tex]
[tex] (f + g)(x) = (2x^2 - 4) + (6x - 3) [/tex]
Combine like terms:
[tex] (f + g)(x) = 2x^2 + 6x - 7 [/tex]
Now, evaluate at x = 3:
[tex] (f + g)(3) = 2(3)^2 + 6(3) - 7 [/tex]
[tex] (f + g)(3) = 18 + 18 - 7 [/tex]
[tex] (f + g)(3) = 29 [/tex]
So, (f + g)(3) = 29.
2. (fg)(-1):
[tex] (fg)(x) = f(x) \cdot g(x) [/tex]
[tex] (fg)(x) = (2x^2 - 4) \cdot (6x - 3) [/tex]
Expand and simplify:
[tex] (fg)(x) = 12x^3 - 6x^2 - 24x + 12 [/tex]
Now, evaluate at x = -1:
[tex] (fg)(-1) = 12(-1)^3 - 6(-1)^2 - 24(-1) + 12 [/tex]
[tex] (fg)(-1) = -12 - 6 + 24 + 12 [/tex]
[tex] (fg)(-1) = 18 [/tex]
So, (fg)(-1) = 18.
Therefore, the correct answer is:
B. (fg)(-1) = 18.