For the given function f,g, and h, find f*g*h and state the exact domain of f*g*h
f(x)=e^x
g(x)=log_x
h(x)=x/x+8
To find f*g*h, we need to first perform the individual multiplications of f, g, and h, and then multiply the results together.
1. f(x) = e^x
2. g(x) = log_x
3. h(x) = x/(x+8)
First, we multiply f(x) and g(x) as follows:
f(x) * g(x) = (e^x) * (log_x)
Next, we multiply the result of f(x) * g(x) by h(x):
(f(x) * g(x)) * h(x) = (e^x * log_x) * (x/(x+8))
To find the exact domain of f*g*h, we need to take into consideration the domains of individual functions.
1. Domain of f(x) = all real numbers (-∞, +∞)
2. Domain of g(x) = (0, +∞) [as log_x is only defined for positive numbers]
3. Domain of h(x) = (-∞, -8) U (-8, +∞) [as x/x+8 will be undefined at x = -8]
Since f(x) * g(x) * h(x) involves the multiplication of all three functions, the domain of f*g*h will be the intersection of the domains of f(x), g(x), and h(x).
Domain of f*g*h = (0, +∞) U (-∞, -8) U (-8, +∞)
This means that the exact domain of f*g*h consists of all real numbers except for -8.