Posted by Trina on Wednesday, March 27, 2013 at 2:30pm.
If f(x)lnx,g(x)=e^8x, and h(x)=x^7, find the following:
a. (f.g)(x). what is the domain of f.g?
b.(g.f)(x). what is the domain of g.f?
c. (f.h)(x). what is the domain of f.h?
I have no clue how to do this. Somebody please help me?? please???

Math  Steve, Wednesday, March 27, 2013 at 2:53pm
how can you get this far and have no clue? Just think of the stuff you have been studying. In particular, the most recent exercises. Surely there are some examples of thing similar to these. That's why they're asking these questions.
I assume by f.g you mean f◦g. So,
f◦g = f(g) = ln(g) = ln(e^8x) = 8x
g◦f = e^(8f) = e^(8lnx) = (e^lnx)^8 = x^8
f◦h = ln(h) = ln(x^7) = 7lnx
The domain of those should be easy.

Math  Staci, Wednesday, March 27, 2013 at 3:35pm
unfortunetly, none of this comes natural to me so the domains are especially difficult for me too.

Math  Steve, Wednesday, March 27, 2013 at 11:36pm
the domain of all polynomials is all reals. There's no number where f(x) is undefined.
For rational functions (the quotient of two polynomials p(x)/q(x)) the domain is all reals except where q(x)=0 because division by zero is undefined.
For functions with square roots (or any evenpowered root) and logs the value must be positive, since square root is undefined for negative numbers.
That covers most of the common cases.
For your problems, f(g) and g(f) have domain all reals. h has domain all x>0, as does f(x) and f(h). After all f(h(3)) is undefined since h(3) is negative.
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