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).(Enter your answer using interval notation.)

C)Find (f − g)(x).

D)Find the domain of (f − g)(x)(Enter your answer using interval notation.)

E)Find (fg)(x).

F)Find the domain of (fg)(x)(Enter your answer using interval notation.)

G)Find (f/g)(x)

E) Find the domain of (f/g)(x)(Enter your answer using interval notation.)

Answer 1

The function "f" is the same as "x" because f(x) = x and the function "g" is the same as "5x" because g(x) = 5x.

So f + g = x + 5x = 6x

And f - g = x - 5x = -4x

And fg = f•g = x•5x = 5x²

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

For the first 3, there are no domain restrictions so the domain is (-∞, ∞) but for the 4th one, since it begins with "x/(5x)" and division by zero is not allowed, the domain is restricted to all numbers except zero or (-∞, 0) U (0, ∞). If x = 0, then "x/(5x)" would result in a division by zero when "x" is plugged in. Notice that you need to determine the domain prior to simplification!