Respuesta :
Answer: fg [tex]=x^3+4x^2-16x-64[/tex] and
Domain: All real number. All real number or [tex](-\infty,\infty)[/tex]
Explanation:
fg means product of two given function f(x) and g(x)
where,
[tex]f(x)=x^2-16 [/tex] and [tex]g(x)=x+4[/tex]
Now, we have to find fg
So, fg=[tex]f(x)\times g(x)[/tex]
Substitute f(x) and f(x)
[tex] \Rightarrow (x^2-16)(x+4)[/tex]
Using distributive property simplify above expression and we get,
[tex] \Rightarrow x^3+4x^2-16x-64[/tex]
We can see it is cubic polynomial. So, domain of cubic polynomial is all real number.
Domain: All real number or [tex](-\infty,\infty)[/tex]
Answer: x+4; all real numbers except =-4
Step-by-step explanation:
f(x)/g(x) = (x2-16)/(x+4)
The domain is all real numbers except x = -4 (because the denominator is zero at x = -4 and division by zero is undefined.)
We can simplify by factoring the numerator:
(x2-16)/(x+4) = (x-4)(x+4)/(x+4) = (x-4)
The domain is the same as the original expression: all real numbers except x = -4
