It is not unusual to have to solve a problem involving a composite function, and such a situation is considered in this exercise. Suppose one wants to find the value(s) of  where  = 0. However,  is...

It is not unusual to have to solve a problem involving a composite function, and such a situation is considered in this exercise. Suppose one wants to find the value(s) of
 where = 0. However, is given in terms of a variable, and there is a second equation that determines the value of
 for any given value of
. In this exercise, let
=

³
+ 3 + 1, where

So, given
, to evaluate one first solves the above equation for
 and then substitutes this into the formula for
. Although this might appear to an artificially complex question, as will be explained in Section 9.5, it is a fairly common question that arises in applications.

(a) Describe how to use the bisection method to find the value of
 where
 = 0. Make sure to explain how you find the initial interval.

(b) Writing
 as
, explain how to use Newton’s method to find the value of
 where
 = 0.

(c) Using MATLAB, find the value of where
 = 0.