Let , and consider the function F_ a (x)= _ a (x^ 2 -4)+ x+a x-1 . (i) Write the…

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let a>0,  a≠1a>0,\;a\neq1, and consider the function Fa(x)=log⁡a(x2−4)+x+ax−1.F_{a}(x)=\log_{a}(x^{2}-4)+\sqrt{\dfrac{x+a}{x-1}}. (i) Write the condition on xx that allows the logarithmic term to be defined. (ii) Write the pair of conditions that make the radical term real and its denominator non-zero. (iii) For a given aa, solve the system of conditions obtained in parts (i) and (ii). Identify clearly how the resulting set of admissible xx depends on the parameter aa. (iv) Determine all real values of aa for which the domain of FaF_{a} is non-empty, and for each such aa describe the corresponding domain completely.

Related theory

Browse the problem library