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Functions and Their Properties · Paper 2 — Free Maths AA HL Practice Questions

1MasterySAQ-SDefinition and types of functions (one-to-one, onto etc.)s6 marksPaper 2~9 min

The function

g

is defined by

g(x) = \sqrt{9 - x^2}

for

x \in \mathbb{R}

, with its natural domain.

(a)

State the domain and range of

g

. [2 marks]

(b)

Determine whether

g

is one-to-one. Justify your answer. [2 marks]

(c)

The function

h

is defined by

h(x) = \sqrt{9 - x^2}

for

x \in [0, 3]

, with codomain

[0, 3]

. Show that

h

is a bijection (both one-to-one and onto). [2 marks]

Solutions

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