Question

The functions are f(x)= lnx, x>0 and g(x)=sinx. Let H be the composition of f with g, or H(x)=f(g(x)) and

A) Find the domain of H
B) Find the range of H
C) Find the zeros of H

Answer 1

h = ln (sin x)

look at this at x = 0, x = pi/2, x = pi/4, x = 3 pi/4 , x = pi , note sin x must be >0 so only quadrants 1 and 2

ln sin 0 undefined !
ln sin pi/4 = -.346
ln sin pi/2 = 0
ln sin 3 pi/4 = -.346
etc :)