If fx ln x gX e6x and hx x5 find the following f gx what

If f(x) = ln x, g(X) = e^6x, and h(x) = x^5, find the following. (f g)(x) what is the domain of f g? (g f)(x) What is the domain of g f? (f h)(x) What is the domain of f h? Find (f g)(x) What is the domain of f g? (Type your answer in interval notation) Find (g f)(x) (Simply your answer.) What is the domain of g g? (Type your answer in interval notation) Find (f h)(x) (Simplify your answer) What is the domain of f h? (Type your answer in interval notation)

Solution

f(x) = ln(x) ; g(x) = e^6x ; h(x) = x^5

a) ( f o g)(x) = ln(e^6x)

= 6xln(e)

= 6x

Domain :( -inf , inf)

b) (g o f) (x) = e^(6ln(x))

= e^ln(x^6)

= x^6

Domain:( -inf , inf)

c) ( f o h)(x) = ln(x^5)

= 5ln(x)

Domain: x>0

( 0, inf)