Determine the set of all real numbers for which is defined.

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Determine the set of all real numbers for which g(x)=log⁡53x−1x+2g(x)=\log_{5}\sqrt{\dfrac{3x-1}{x+2}} is defined. (a) (−2,∞)(-2,\infty) (b) (−∞,−2)∪[13,∞)(-\infty,-2)\cup\left[\dfrac13,\infty\right) (c) (−∞,−2)∪(13,∞)(-\infty,-2)\cup\left(\dfrac13,\infty\right) (d) (13,∞)\left(\dfrac13,\infty\right)

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