The function
R(x)=x3−6x2+11x−64−x
is defined for certain real values of x.
a. (i) Find the set of all real numbers for which the numerator is defined.
b. (ii) Factorise the denominator completely and list every real number that makes it zero.
c. (iii) Combine the conditions obtained in (i) and (ii) to write the domain of R(x) in interval notation.