Question

Let f(x) = x – 4 and g(x) = x^2 – 16.

Perform the function operation f(x) + g(x) and then find the domain.​

Answer 1

f(x) +g(x) = x^2 +x -20

domain: all real numbers

Explanation:

The sum of two polynomial functions is found by adding the terms of each function definition:

f(x) +g(x) = (x -4) +(x^2 -16)

f(x) +g(x) = x^2 +x -20

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The domain of any polynomial is "all real numbers." The set of polynomials is closed to addition, meaning the sum of any polynomials is another polynomial. The sum, too, will have a domain of "all real numbers."