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)

## Answer this Question

## Related Questions

- precalculus - For the given functions f ,g , and h , find fogoh and state the ...
- precal - For the given functions f ,g and h, find f o g o h and state the exact ...
- precalculus - given functions f,g, and h find f o g o h state exact domain. show...
- pre calculus - Having a bit of a problem with this for the given functions f, g ...
- Math 4 - For the given functions f(x) = ln(x) , g(x) = |x| - 7, h(x)=5x+6 find f...
- Calculus - Find the sum and difference functions f + g and f – g for the ...
- college algebra - For the given functions f and g find the following and state ...
- calculus - for the given functions f&g, find the following and state the domain ...
- MATH - for the given functions f and g find the following and state the domain ...
- Math - for the given functions f and g find the following and state the domain ...