Question

Let f(x) = 2x² + 14x – 16 and g(x) = x+8. Perform the function operation and then find the domain of the result.(x) = (simplify your answer.)

Answer 1

We need to find the following division of the functions f(x) and g(x):

`(f)/(g)(x)=(f(x))/(g(x))=(2x^2+14x-16)/(x+8)`

We can note that the numerator can be rewritten as

`2x^2+14x-16=2(x^2+7x-8)=2(x+8)(x-1)`

Then the division can be written as:

`(f)/(g)(x)=(f(x))/(g(x))=(2(x+8)(x-1))/(x+8)`

From this result, we can cancel out the term (x+8) from both sides and get,

`(f)/(g)(x)=(f(x))/(g(x))=2(x-1)`

Therefore, the result of the division is:

`(f)/(g)(x)=2(x-1)`

which domain is all real numbers:

`x\in(-\infty,\infty)`