You did letter B for me, can you check my work?
posted by For Reiny .
if f(x)=lnx, g(x)=e^3x, and h(x)=x^4 find following
A)(f of g)(x)and the domain of f of g
B) (g of f)(x) and the domain of g of f
C) (f of h)(x) and the domain of f of h
A) f(g(x))
=lnx(e^3x)
domain x>0
C)f(h(x))
=lnx(x^4)
x>4

A) close , but not quite
f(g(x))
= f(e^3x)
= ln (e^(3x)) , you have an extra x in there
f(x) was defined as lnx, so whatever x is replaced by on the left side, must be replaced by on the right side ....e.g.
f(2) = ln2
f(happy face) = ln(happy face)
f(e^3x) = ln(e^3x)
C) you made the same error
f(h(x)) = f(x^4) = ln x^4
the domain would be x > 0 
i understand now thank you