2026 CCHY P2 Q5

2026 CCHY P2 Q5

Secondary 4
5 marks

The function is defined by \(f(x)=\sqrt{x^2+4}\), where \(x>0\).

  1. Explain whether \(f(x)\) is an increasing or decreasing function.[4]
  2. Hence explain why the equation \(\sqrt{x^2+4}\) has at most one solution for every number \(k\), where \(x>0\).[1]

Solution:

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Answer:(a) Strictly increasing for \(x>0\). (b) For the intended equation \(f(x)=k\), at most one solution.

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