Question

Let f(x) = 16 – x^2, g(x) = 4 – x. Find (fg)(x) and its domain.

Answer 1

x+4; all real numbers except =-4

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