Question

F(x) = 3x^2 + 6x - 5
g(x) = 423 - 5x^2 + 6
Find (f + g)(x).

Answer 1

The sum of the functions f(x) = 3x^2 + 6x - 5 and g(x) = 423 - 5x^2 + 6 is (f + g)(x) = -2x^2 + 6x + 424.

Step-by-step explanation:

The question involves the addition of two functions f(x) = 3x^2 + 6x - 5 and g(x) = 423 - 5x^2 + 6. To find (f + g)(x), we simply add the corresponding terms from each function:

• Add the quadratic terms: 3x^2 from f(x) and -5x^2 from g(x) to get -2x^2.
• Add the linear terms: 6x from f(x) and no linear term from g(x), so we still have 6x.
• Add the constant terms: -5 from f(x) and 423 + 6 from g(x) to get 424.

Combining these results, the function (f + g)(x) is (f + g)(x) = -2x^2 + 6x + 424.