Question

. For the given functions f, g, and h , find f o g o h and state the exact domain of f o g o h . Please show all of your work. f(x)=lnx, g(x)=|x|-2, h(x)=4x-7

Answer 1

So here we go
\[f ogoh(x)=f(g(h(x)))=\ln(|4x-7|-2)\rightarrow |4x-7|-2>0\]so\[4x-7>2\rightarrow x>9/4\]or\[4x-7<-2\rightarrow x<5/4\]so\[dom (fogoh)=(-\infty,5/4)\cup(9/4,\infty)\]

Answer 2

The first two functions have unrestricted domains, but the third (f(x)) requires a strictly positive input.