TMUA Style, Advanced (Paper 1)

TMUA Style Questions · Mathematical Knowledge · Advanced

This free ExamAlly page is a full TMUA Style practice question for students preparing for the TMUA (Test of Mathematics for University Admission). It mirrors the multi-topic style of the real exam: you choose a method, work through every option, and review a step-by-step solution—no account required.

Independent practice material, not affiliated with official TMUA organisers.

Let $f(x)=\dfrac{\sqrt{ax+5}}{x-1}$ , where $a\in\mathbb{R}$ and $f$ is defined wherever the expression is real. Suppose $f$ is decreasing on its whole domain (i.e., on each connected component of its domain). Which of the following gives the complete condition on $a$ for this to hold?

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