if f(x)=lnx, g(x)=e^3x, and h(x)=x^4 find following

Question

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

please show work

Answer 1

I will do B), you do the others the same way ...

b)
(g of f)(x) to me means g(f(x))
= g(lnx)
= e^(3lnx)

since we can only take logs of positive numbers,
domain: x > 0
range: I hope you are familiar with the basic exponential function, so y>0