Question

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

f(x)=square root x; g(x)=5x-1

a. (f*g)(x)= ?
what is the domain of f*g?

b. (f/g)(x)=?
what is the domain of f/g?

please show work

Answer 1

domains:
f: x>=0
g: all real

f*g = f(x)*g(x) = (5x-1)√x
domain: x>=0

f/g = f(x)/g(x) = √x / (5x-1)
domain x>0 but x ≠ 1/5
That is, (0,1/5)U(1/5,oo)

Answer 2

Describe the domain of the function f (X) =x+4/x square_1 solve the problem