Question

If f(x)= ln x, g(x) = e^3x, and h(x) = x^7, find the following...

a) (fog)(x) What is the domain of fog?
b) (gof)(x) What is the domain of gof?
c)(foh) What is the domain of foh?

Answer 1

a)
f(g) = ln(g) = ln(e^3x) = 3x

b)
g(f) = e^(3f) = e^(3lnx) = e^(ln(x^3)) = x^3

c)
f(h) = ln(h) = ln(x^7) = 7lnx

you can prolly work out the domains. Just remember that the domain of f and of g must be considered when deciding on the domain of (f◦g). If you have trouble, some on back and show where you get stuck.