precal
posted by Jo on .
For the given functions f, g, and h, find fogoh and state the exact domain of fogoh. Please show all of your work.
f(x)=lnx
g(x)=x2
h(x)=4x7

domains:
f: x>0
g: all reals
h: all reals
f(x) = lnx
f(g(h)) = ln(g(h))
= ln(h2)
= ln(4x72)
ln(u) is defined only for u>0
so, we need 4x72 > 0
4x7 > 2
so, if 4x7>=0 (or x>=7/4), 4x7 > 2 ==> x > 9/4
or, if 4x7 < 0 (or x<7/4), (4x7) > 2 ==> x < 5/4
so, domain is (oo,5/4) U [9/4,oo)