Assistance in Algebra 2

Question

if f(x) = In x, g(x) = e^4x, and h(x) = x⁵

 

I can't seem to find the domain of

a. (f.g)(x)

b. (g.f)(x)

c. (f.h)(x)

 

 

 

Answer 1

f(x) = lnx g(x) = e^4x h(x) = x^5

(fog)(x) = f(g(x)) = ln(e^4x) = 4x

(God)(x) = g(f(x)) = e^4(lnx) = e^lnx(e^lnx)(e^lnx)(e^lnx) = x(x)(x)(x) = x^4

(foh)(x) = f(h(x)) = ln(x^5) = 5lnx