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 even-powered 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.

## Answer this Question

## Related Questions

- You did letter B for me, can you check my work? - if f(x)=lnx, g(x)=e^3x, and h(...
- algebra - if f(x)=lnx, g(x)=e^3x, and h(x)=x^4 find following A)(f of g)(x)and ...
- college alg :( - if f(x)=lnx, g(x)=e^3x, and h(x)=x^4 find following A)(f of g)(...
- Math - The domain of g(x) is -1< x < 9 What is the domain of g(x - 4) I ...
- Pre-Calc - Suppose that f has a domain of A and g has a domain of B. (a). What ...
- math - For the given functions f & g find the following and state the domain of ...
- 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 ...
- Small Group Communication - Regulating participation, climate making, and ...
- college algebra - 1.for the given function f&g, find the following and state the...