Consider the equation x y 2 y Which of the following statements are not correct ...........

Mathematics (NDA) Relations and Functions

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Consider the equation x + | y | = 2 y

Which of the following statements are not correct?

1. y as a function of x is not defined for all real x.

2. y as a function of x is not continuous at x = 0.

3. y as a function of x is differentiable for all x.

Select the correct answer using the codes given below.

1 and 2

2 and 3

1 and 3

1, 2 and 3

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Explanation:

Given, x + | y|= 2y
x + y = 2y, for y > 0
=> y = x
and x − y = 2y, for y < 0
=> y = 1/3 x
Graph of x + | y|= 2y
From the graph:
y as a function x defined for all real x
and y as function of x is not differentiable at x = 0
$\therefore$ Statements 1 and 3 are incorrect.