Question

Find the formula for (f + g)(x) and simplify your answer. Then find the domain for (f + g)(x). Round your answer to two decimal places, if necessary.

Answer 1

Answers: (f+g)(x)=x²+4-4x

Domain = (-∞, ∞)

Explanation:

(f + g)(x) is equal to f(x) + g(x). Where f(x) is x²+4 and g(x) is -4x.

Then:

$\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(x^2+4)+(-4x) \\ (f+g)(x)=x^2+4-4x \end{gathered}$

Now, the domain is the set of all the values where (f+g)(x) is defined.

Since (f+g)(x) is a polynomial, the domain is the set of all real numbers or:

( - ∞, ∞)