Question

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

Answer 1

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

Answer 2

i understand now thank you