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Functions and Their Properties · Paper 3 — Free Maths AA HL Practice Questions

1ChallengeLAQDomain and range of functionss10 marksPaper 3~15 min

Consider the function

f(x) = \sqrt{\ln\!\left(\dfrac{x+1}{x-1}\right)}

, where

x \in \mathbb{R}

(a)

Determine the maximal domain of

f

, expressing your answer in exact form. [3 marks]

(b)

For the function

g(x) = f(x) + \sqrt{4 - x^2}

, find the domain of

g

. [2 marks]

(c)

Prove that the range of

f

[0, \infty)

. You must justify continuity and use a formal argument (such as the Intermediate Value Theorem or strict monotonicity) to establish that all values in

[0, \infty)

are attained. [5 marks]

Solutions

Questions 2-11

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