Question

for the functions f(x)=5 - x² and g(x)=x² + 6x - 27, find f + g, f - g, fg, and f/g. determine the domain for each function.
(f + g)(x)=6x - 22 (simplify your answer.)
what is the domain of f + g? select the correct choice below and, if necessary, fill in the answer box to complete your
a. the domain of f + g is { }. (use a comma to separate answers as needed.)
b. the domain of f + g is . (type your answer in interval notation.)
c. the domain of f + g is ∅.
(f - g)(x)= (simplify your answer.)

Explanation:

Step1: Recall domain of polynomial functions

Polynomial functions are defined for all real - numbers.

Step2: Analyze \(f + g\)

\((f + g)(x)=6x - 22\) is a polynomial function.

for \((f - g)(x)\):

Step1: Subtract \(g(x)\) from \(f(x)\)

\((f - g)(x)=(5 - x^{2})-(x^{2}+6x - 27)\)

Step2: Simplify the expression

\[

$$\begin{align*} (f - g)(x)&=5 - x^{2}-x^{2}-6x + 27\\ &=-2x^{2}-6x + 32 \end{align*}$$

\]

Answer:

B. The domain of \(f + g\) is \((-\infty,\infty)\)