how to find given function f and g

Question

for the given function f and g, find the following and state the domain of each result

f(x)=sqrt x;  g(x)=5x-8

A. what is the domain of f*g

B. (f/g)x=

what is the domain of f/g

Answer 1

A

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

(fg) (x) = Sqrt(x) * (5x-8)

Domain is the set of possible x numbers.  You can't have a negative inside the square root, so the domain is x greater than or equal to 0.

B

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

(f/g) (x) = Sqrt(x) / (5x-8)

x can't be negative (the square root is still there).

The bottom of the fraction can't be 0, so:

5x - 8 = 0

5x = 8

x = 5/8

x can't be 5/8

Domain is x such that x is greater than or equal to 0 and x is not equal to 5/8