The function R(x)= 4-x x^ 3 -6x^ 2 +11x-6 is defined for certain real values of .

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

The function R(x)=4−xx3−6x2+11x−6R(x)=\frac{\sqrt{4-x}}{x^{3}-6x^{2}+11x-6} is defined for certain real values of xx. (i) Find the set of all real numbers for which the numerator is defined. (ii) Factorise the denominator completely and list every real number that makes it zero. (iii) Combine the conditions obtained in (i) and (ii) to write the domain of R(x)R(x) in interval notation.

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