For the given functions find f and g, find the following and state the domain of each result.

Question

f(x)=sqaure root of x; g(x)=3x-2

A) (f*g)(x)=

 What is the domain? of f*g?

B)(f/g)(x)=

What is the domain of f/g?

Answer 1

• For the function f + g, f - g, f * g, the domains are defined as the inrersection of the domains of f and g.
• For f/g, the domains is the intersection of the domains of f and g except for the points where g(x) = 0

(A).

The functions are f(x) = √x and g(x) = 3x - 2.

(f * g)(x) = f(x) * g(x)

               = (√x) * (3x - 2)

               = 3x√x - 2√x.

The domain of f(x) = √x is [0, +∞)

The domain of g(x) = 3x - 2 is (-∞, +∞)

The domain of (f * g)(x) is [0, +∞) ∩ (-∞, +∞) = [0, +∞).

 

(B).

The functions are f(x) = √x and g(x) = 3x - 2.

(f/g)(x) = f(x) / g(x)

            = (√x) / (3x - 2)

The denominators not equals to zero.

3x - 2 ≠ 0

x ≠ 2/3.

The domain of f(x) = √x is [0, +∞)

The domain of g(x) = 3x - 2 is (-∞, +∞)

The domain of (f / g)(x) is {[0, +∞) ∩ (-∞, +∞)} - 2/3 = [0, +∞) - 2/3.