A real valued function f is defined as f(x)={\\begin{array}{ccc}-1 & & -2 \leq x \leq 0 \ x-1 & & 0&lt\ x \leq 2\end{array}.. Which of the following statement is FALSE?

Correct Answer is : f(|x|)+|f(x)|=1, if 0≤x≤1

f(|x|)=|x|-1, if 0 \leq x \leq 1

f(|x|)+|f(x)|=1, if 0 \leq x \leq 1

f(|x|)-|f(x)|=0, if 1 \leq x \leq 2

NIMCET 2023 Question Paper with solutions

Question : 26 of 120

Marks: +1, -0

A real valued function

f

is defined as

f(x)={\{\table -1, , -2 ≤ x ≤ 0 ; x-1, , 0< x ≤ 2}.

. Which of the following statement is FALSE?

Solution:

Graphical solution:

Add these two graphs

y=|f(x)|+f(|x|)

From given graphs we can find that statement (C) is false.

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