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CAT 2017 [slot 1] Question with solution 30

Question 30:
The shortest distance of the point $(\frac{1}{2},1)$ from the curve y = I x -1I + I x + 1I is
  1. 1
  2. 0
  3. $\sqrt{2}$
  4. $\sqrt{\frac{3}{2}}$
Option: 1
Explanation:

The graph of the given function is as shown below.

The graph of $y = | x - 1 | + | x + 1 |$ is shown above. The shortest distance of $\left( \frac { 1 } { 2 } , 1 \right)$ from the graph is 1


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