Find the following fx 5x 8 gx 4 x a f gx b f gx c fgx

Find the following.

f(x) = 5x 8,     g(x) = 4 x

(a)    (f + g)(x) =

(b)    (f g)(x) =

(c)    (fg)(x) =

(d)    (f/g)(x) =

What is the domain of f/g?

Solution

f(x) = 5x 8,     g(x) = 4 x

a) (f + g)(x) = f(x) + g(x) = 5x - 8 + 4 - x = 4x - 4

(b)    (f g)(x) = f(x) - g(x) = 5x - 8 - 4 + x = 6x - 12

(c)    (fg)(x) = f(x)*g(x) = (5x - 8)*(4 - x) = -5x^2 + 28x - 32

(d)    (f/g)(x) =  f(x)/g(x) = (5x - 8)/(4 - x)

Domain of (f/g)(x) =======> x < 4 or x > 4