Answer the following questions for the function, r ( x ) = 3 x − 18/x^2+5 x+6 ? a)What is the domain of r ( x ) ? Give your answer using interval notation. b)r ( − 4 ) = c)For what value(s) of x does r ( x ) = 0 ? x= d)r ( x ) = − 3 5 . What is x ? x =
It is given
(a) The maximum domain of a function represents all the values it can take without becoming undefined/undetermined.
In our case, we see that
#r(0) = 6-18/0 -> " Undefined"#
As such, the domain of
(c) We wish to find the roots of
This is going to be a bit tricky. First of all, multiply both sides by
See this link on how to solve this cubic equation.
Finally, we find out the only root of
I won't even try to solve this. By trial and error, you can approximate the roots of our new formed equation; for a fact, it has
Anyway, here are the three values of