First slide

Introduction to real valued functions

Question

Number of solutions of the equation $| 2 - | x ∥ = x + 4$ is

Moderate

A

0
B

1
C

2
D

Infinite

Solution

$\begin{array}{l} | 2 - | x ∥ = x + 4 (i) \\ \Rightarrow 2 - | x | = x + 4 (ii) \\ or | x | - 2 = x + 4 (iii) \end{array}$
From (i) $2 - x = x + 4 or x = - 1$
But this value does not satisfy (i).
From (iii), $- x - 2 = x + 4 or x = - 3,$ which satisfies (i).
So, equation has only one solution.

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