if fx In x gxe7x and hxx6 find the following f o gx what is

if f(x)= In x, g(x)+e^7x, and h(x)=x^6 find the following

( f o g)(x) what is the domain of f o g

(g o f)(x) what is the domain of g o f

(f o g)(x) what is the domain of f o h

Solution

f(x) = ln(x) ; g(x) = e^7x ; h(x) = x^6

a) ( f o g)(x) = ln(e^7x)

= 7xln(e)

= 7x

Domain :( -inf , inf)

b) (g o f) (x) = e^(7ln(x))

= e^ln(x^7)

= x^7

Domain:( -inf , inf)

c) ( f o h)(x) = ln(x^6)

= 6ln(x)

Domain: x>0

( 0, inf)