Find fx Let fx X 6 and gx 3x 4 Find the following a f g

Find f(x)

Let f(x) = X - 6 and g(x) = 3x + 4. Find the following. (a) (f + g) (x) (b) (f - h) (x) (c) (f middot g) (x) (d) (f/g) (x) (e) The domain of f/g (a) (f + g)(x) = (Simplify your answer. Do not factor.) (b) (f - g)(x) = (Simplify your answer. Do not factor.) (c) (f middot g)(x) = (Simplify your answer. Do not factor.) (d) (f/g) (x) = (Simplify your answer. Do not factor.) (e) The domain of f/g is (Type your answer in interval notation.)

Solution

(f+g)x = f(x) + g(x) = x² - 6 + 3x + 4 = x² + 3x - 2

(f-g)x = f(x) - g(x) = x² - 6 - 3x -4 = x² - 3x -10

(f.g)x = f(x)*g(x) = (x² - 6 )*(3x + 4) = 7x² -18x - 24

(f/g)x = f(x)/g(x) = (x² - 6 )/(3x + 4)