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

Question

(1 point)

x + 4; all real numbers except x # 4

x + 4; all real numbers except x # -4

x -4; all real numbers except x # 4

x - 4; all real numbers except x # -4

Answer 1

To find f/g, we need to divide f(x) by g(x).

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

However, there is a restriction on the domain of f/g. We cannot divide by zero, so x + 4 cannot equal zero.

Hence, the domain of f/g is all real numbers except x = -4.

So, the correct answer is:

x + 4; all real numbers except x = -4

Answer 2

No, wrong again.
(x^2 - 16)/(x+4) = x-4 for x ≠ -4

Answer 3

Apologies for the previous incorrect response.

You are correct. To find f/g, we divide f(x) by g(x):

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

To simplify this expression, we can factor the numerator:

f(x)/g(x) = ((x + 4)(x - 4))/(x + 4)

Simplifying further, we can cancel out the common factor of (x + 4):

f(x)/g(x) = x - 4

So, the correct answer is:
f/g = x - 4

And the domain of f/g is all real numbers except x = -4.