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GATE 2023 IN – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Which of the figures P, Q, R, S represents $f(x)=\bigl||x+2|-|x-1|\bigr|$?

Diagram for GATE 2023 IN question 9
  1. P
  2. Q
  3. R
  4. S

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Show answer and explanation

Correct answer: (A) P

Explanation

For $x\le-2$ and $x\ge1$, the outer absolute value gives 3. For $-2\le x\le1$, it gives $|2x+1|$, with minimum zero at $x=-1/2$.

Thus two horizontal plateaus flank a V-shaped valley, as in **P, A**.