Given fx 4 lnx and gx e3x find the following f g 3 g f2

Given f(x) = 4 ln(x) and g(x) = e^3x, find the following: (f g) (3) = (g f)(2) =

Solution

f(x)= 4ln x

g(x)= e^3x

(fog)(x) = f(g(x))= f(e^3x)= 4 ln e^3x= 4*3x=12x

(fog)(2) = 12*2=24

b. gof(2)

gof(x)=g(f(x)) = g(4 lnx)

                      = e^{3(4 lnx)} = e^{lnx^12}

                                        x¹²

gof(2)=2^12=4096