Question

for the functions f(x)=5 - x^2 and g(x)=x^2 + 6x - 27, find f + g, f - g, fg, and $\frac{f}{g}$. 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 choice. 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)=5 - x^2 (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 choice.

Explanation:

Step1: Find (f - g)(x)

(f - g)(x)=f(x)-g(x)=(5 - x^{2})-(x^{2}+6x - 27)=5 - x^{2}-x^{2}-6x + 27=-2x^{2}-6x + 32

Step2: Determine domain of f - g

The functions f(x) = 5 - x^{2} and g(x)=x^{2}+6x - 27 are both polynomials. The difference of two polynomials is also a polynomial. Polynomials are defined for all real - numbers.

Answer:

(f - g)(x)=-2x^{2}-6x + 32
The domain of f - g is B. (-∞,∞)