SOLUTION: Given the functions, {{{ f(x) = x-4 }}} and {{{ g(x)=(x+2)/(x-2) }}}, determine an expression for h(x) such that {{{ h(x)=(f*g/g)(x) }}}. Having trouble with this practice quest

Algebra ->  Functions -> SOLUTION: Given the functions, {{{ f(x) = x-4 }}} and {{{ g(x)=(x+2)/(x-2) }}}, determine an expression for h(x) such that {{{ h(x)=(f*g/g)(x) }}}. Having trouble with this practice quest      Log On


   

Question 949689: Given the functions, +f%28x%29+=+x-4+ and +g%28x%29=%28x%2B2%29%2F%28x-2%29+, determine an expression for h(x) such that +h%28x%29=%28f%2Ag%2Fg%29%28x%29+.
Having trouble with this practice question, please help.
Thank you
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Plug everything in and simplify. Just fitting the formula shown and some algebra steps.

Here is the raw unsimplified form:

%28%28%28x%2B2%29%2F%28x-2%29%29-4%29%2F%28%28x%2B2%29%2F%28x-2%29%29

Examine that expression to see how it is made.
The numerator is the composition f%28g%28x%29%29 as shown in that part for h(x).
The denominator is g%28x%29 as shown in that other part of h%28x%29.

The most important thing to be able is to form that expression for h(x) as defined. The next thing to do is to simplify that expression.