Posted by Jo on Wednesday, January 18, 2012 at 3:10am.
domains:
f: x>0
g: all reals
h: all reals
f(x) = lnx
f(g(h)) = ln(g(h))
= ln(|h|-2)
= ln(|4x-7|-2)
ln(u) is defined only for u>0
so, we need |4x-7|-2 > 0
|4x-7| > 2
so, if 4x-7>=0 (or x>=7/4), 4x-7 > 2 ==> x > 9/4
or, if 4x-7 < 0 (or x<7/4), -(4x-7) > 2 ==> x < 5/4
so, domain is (-oo,5/4) U [9/4,oo)
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