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)`

Step-by-step 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)* 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)`