Analysis and Approaches for IBDP Maths Ebook 2 | Page 73

23
Paper 1 Section A – Inverse Trigonometric Functions
Example
x
The function f is defined by f ( x) � arccos( e ) .
(a) Find the largest possible domain of f .
(b) Find f
1 ( x)
.
�
[2]
[3]
Solution
x
(a) �1� e � 1
A1
x 0
0 �e
� e
x � 0
Thus, the largest possible domain of f is
{ x: x� 0} . A1
x
(b) y�
arccos( e )
y
�x� arccos( e )
(M1) for swapping variables
y
cos x� e
M1
y�
ln cos x
�
�f 1 ( x) � ln cos x
A1
[2]
[3]
7
Exercise 23
1. The function f is defined by f ( x) � 1� tan x .
(a) Find the largest possible domain of f .
(b) Find f
1 ( x)
.
�
[2]
[3]
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