Consider the following functions. f(x)=4/x, g(x)=6/x+6

Question

f(x)=4/x, g(x)=6/x+6

A) Find (f + g)(x).

B)Find the domain of (f+ g)(x)

C) Find (f − g)(x)

D)Find the domain of (f − g)(x)

E) Find (fg)(x)

F)Find the domain of (fg)(x

G)Find (f/g)(x)

H) Find the domain of (f/g)(x)

Answer 1

A) (f + g)(x) = f(x) + g(x) = 4/x + 6/(x + 6)

B) The domain of (f + g)(x) is all real numbers except x = 0 and x = -6, since division by zero is undefined.

C) (f − g)(x) = f(x) − g(x) = 4/x − 6/(x + 6)

D) The domain of (f − g)(x) is all real numbers except x = 0 and x = -6, since division by zero is undefined.

E) (fg)(x) = f(x)g(x) = (4/x)(6/(x + 6)) = 24/[(x)(x + 6)]

F) The domain of (fg)(x) is all real numbers except x = 0 and x = -6, since division by zero is undefined.

G) (f/g)(x) = f(x)/g(x) = (4/x)/[6/(x + 6)] = 2(x + 6)/3x

H) The domain of (f/g)(x) is all real numbers except x = 0 and x = -6, since division by zero is undefined.