Answer:
Given:
f(x) = 3x² + 1
g(x) = x + 4
Find
(f + g)(x) =
= f(x) + g(x)
= (3x² + 1) + (x + 4)
= 3x² + x + 5
(f - g)(x) =
= f(x) - g(x)
= (3x² + 1) - (x + 4)
= 3x² - x - 3
Domain is what value of x can exist in your function. In other word, is there any gaps in your functions where you function does not exist?
For (f + g)(x) = 3x² + x + 5
The domain is All Real Numbers since there is no x-value in that function where your function will be undefined.
For (f - g)(x) = 3x² - x - 3
The domain is also All Real Numbers since there is no x-value in that function where your function will be undefined.
(f + g)(x) = 3x² + x + 5
(f + g)(-5) = 3(-5)² + (-5) + 5
(f + g)(-5) = 3(25) + 0
(f + g)(-5) = 75
(f - g)(x) = 3x² - x - 3
(f - g)(-5) = 3(-5)² - (-5) - 3
(f - g)(-5) = 3(25) + 5 - 3
(f - g)(-5) = 75 + 2
(f - g)(-5) = 77
