Help. Let f(x) = x2 – 16 and g(x) = x + 4. Find f/g and its domain. A. x + 4; all real numbers except x ≠ –4 B. x – 4; all real numbers except x ≠ –4 C. x - 4; all real numbers …

Question

asked Dec 23, 2018 159k views

1 Answer

Wannes Rosiers · Answer 1 · 2018-12-29T18:33:47+0000

Answer: The correct option is B, i.e., x – 4; all real numbers except x ≠ –4.

Step-by-step explanation:

It is given that,

f(x)=x^2-16

g(x)=x+4

We have to find the function
(f)/(g) .

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

Using
a^2-b^2=(a-b)(a+b)

(f(x))/(g(x)) =((x-4)(x+4))/(x+4)

(f(x))/(g(x)) =x-4

Hence the fountain
(f)/(g) is (x-4).

The domain of
(f)/(g) is the intersection of domain of both function except the the values for which the value of denominator function 0.

Since the domain of f(x) and g(x) is all real numbers but the g(x) is 0 at x=-4, therefore the domain of
(f)/(g) is all real numbers except x ≠ –4.

Therefore, the correct option is B.