Question

Let f(x) = x2 – 16 and g(x) = x + 4. Find fg f g and its domain.

Answer 1

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

Answer 2

Answer: fg $=x^3+4x^2-16x-64$ and

Domain: All real number. All real number or $(-\infty,\infty)$

Explanation:

fg means product of two given function f(x) and g(x)

where,  

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

Now, we have to find fg

So, fg=$f(x)\times g(x)$

Substitute f(x) and f(x)

$\Rightarrow (x^2-16)(x+4)$

Using distributive property simplify above expression and we get,  

$\Rightarrow x^3+4x^2-16x-64$

We can see it is cubic polynomial. So, domain of cubic polynomial is all real number.  

Domain: All real number or $(-\infty,\infty)$