First slide

Functions (XII)

Question

Which of the following statements are incorrect?
$I. If f (x) and g (x) are one-one then f (x) + g (x) is also one-one$
$II. If f (x) and g (x) are one-one then f (x) \cdot g (x) is also one-one$
$III. If f (x) is odd then it is necessarily one-one.$

Moderate

A

$II and III only$
B

$I and II only$
C

$III and I only$
D

$I, II and III$

Solution

$I. f (x) = x and g (x) = - x or f (x) = x and g (x) = - x^{3}$
$II. f (x) = x and g (x) = x^{3}$
$III. f (x) = \sin x which is odd but not one-one or f (x) = x^{2} \sin x which is odd but many-one$

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