Answer: The correct option is B, i.e., x – 4; all real numbers except x ≠ –4.
Explanation:
It is given that,
[tex]f(x)=x^2-16[/tex]
[tex]g(x)=x+4[/tex]
We have to find the function [tex]\frac{f}{g}[/tex].
[tex]\frac{f(x)}{g(x)} =\frac{x^2-16}{x+4}[/tex]
Using [tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex]\frac{f(x)}{g(x)} =\frac{(x-4)(x+4)}{x+4}[/tex]
[tex]\frac{f(x)}{g(x)} =x-4[/tex]
Hence the fountain [tex]\frac{f}{g}[/tex] is (x-4).
The domain of [tex]\frac{f}{g}[/tex] 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 [tex]\frac{f}{g}[/tex] is all real numbers except x ≠ –4.
Therefore, the correct option is B.
