Posted by **Jo** on Wednesday, January 18, 2012 at 3:10am.

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)=|x|-2

h(x)=4x-7

- precal -
**Steve**, Wednesday, January 18, 2012 at 10:46am
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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