Let f(x) = x2 - 16 and g(x) = x+4. Find f/g and its domain.
(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
No, wrong again.
(x^2 - 16)/(x+4) = x-4 for x ≠ -4
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.
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