# 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 =

##### 1 Answer

It is given

#r(x)=3x-18/x^2+5x+6=8x+6-18/x^2#

**(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

#r:RR^"*"#

**(b)**

**(c)** We wish to find the roots of

#r(x)=0#

#8x+6-18/x^2=0#

This is going to be a bit tricky. First of all, multiply both sides by

#8x^3+6x^2-18=0#

#4x^3+3x^2-9=0#

See this link on how to solve this cubic equation.

Finally, we find out the only root of

**(d)**

#8x+6-18/x^2=-35#

#8x^3+6x^2-18=-35x^2#

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