SOLUTION: Let f(x) = √x, g(x) = x + 12 and h(x) = 2/x Find the domain of the following function then simplify the expression. (Enter your answer for the domain using interval not

Algebra ->  Functions -> SOLUTION: Let f(x) = √x, g(x) = x + 12 and h(x) = 2/x Find the domain of the following function then simplify the expression. (Enter your answer for the domain using interval not      Log On


   

Question 1046031: Let
f(x) = √x, g(x) = x + 12 and h(x) = 2/x
Find the domain of the following function then simplify the expression. (Enter your answer for the domain using interval notation.)
(h/g)(x)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The question does not involve f(x).
%28h%2Fg%29%28x%29 means same as h%28x%29%2Fg%28x%29.


h%28x%29%2Fg%28x%29=%282%2Fx%29%2F%28x%2B12%29
x%3C%3E0 AND x%3C%3E-12.
This means domain is (-infinity, -12) U (-12, 0) U (0, infinity).
--
In inequality notation, this is system%28-infinity%3Cx%3C-12%2C-12%3Cx%3C0%2C0%3Cx%3Cinfinity%29.


The ratio of the functions simplified is 2%2F%28x%28x%2B12%29%29=highlight%282%2F%28x%5E2%2B12x%29%29.

Note that you were asked for a RATIO of two functions; NOT a composition of functions.