First slide

Functions (XII)

Question

$Let f : [- 2, 2] \to R be defined by f (x) = \{\begin{array}{cc} - 1, & - 2 \leq x < 0 \\ x - 1, & 0 \leq x \leq 2 \end{array} . Then sum of the roots of the equation f (| x |) = x is$

Moderate

A

-1
B

0
C

$- \frac{1}{2}$
D

1

Solution

$\begin{array}{l} | x | \in [0, 2] \\ ∴ f (| x |) = | x | - 1 = x \\ \Rightarrow x = - \frac{1}{2} \end{array}$

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