Find f + g, f − g, fg, and f/g and their domains. f(x) = x, g(x) = 5x

Question

Find f + g, f − g, fg, and f/g and their domains.

f(x) = x, g(x) = 5x

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)

E) Find the domain of (f/g)(x)

Answer 1

A) (f + g)(x) = f(x) + g(x) = x + 5x = 6x

B) The domain of (f + g)(x) is all real numbers, since there are no restrictions on the domain of x.

C) (f − g)(x) = f(x) − g(x) = x − 5x = −4x

D) The domain of (f − g)(x) is all real numbers, since there are no restrictions on the domain of x.

E) (fg)(x) = f(x)g(x) = x(5x) = 5x^2

F) The domain of (fg)(x) is all real numbers, since there are no restrictions on the domain of x.

G) (f/g)(x) = f(x)/g(x) = x/(5x) = 1/5

E) The domain of (f/g)(x) is all real numbers except x = 0, since division by zero is undefined. Therefore, the domain of (f/g)(x) is (-∞, 0) U (0, ∞).