Question

Given that f() = ²-6-16 and g()=+2, find (f+g)() as a polynomial in its simplest form.

Answer 1

The sum of the two functions f(x) = x^2 - 6x - 16 and g(x) = x + 2 is found by adding them together to get (f+g)(x) = x^2 - 5x - 14 as the simplest form of the polynomial.

Step-by-step explanation:

To find the sum of the functions f(x) = x^2 - 6x - 16 and g(x)= x + 2, we simply need to add the two functions together.

The sum (f+g)(x) is computed by:

1. Add the corresponding terms of the two polynomials.
2. Simplify the expression.

Calculating this gives us:

(f+g)(x) = f(x) + g(x)

= (x^2 - 6x - 16) + (x + 2)

= x^2 - 6x - 16 + x + 2

= x^2 - 5x - 14

This is the polynomial in its simplest form representing the sum of f(x) and g(x).