Number of solutions of $|x - 1| = \cos x$ is

$2$

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$3$

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$4$

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None of the above

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Solution

The correct option is A
$2$

Find the number of solutions to the Equation.
Consider the given Equation
$|x - 1| = \cos x$
Let $y_{1} = |x - 1|$ and $y_{2} = \cos x$ be the two functions.
The graph of these two functions is as shown:
From the above graph, it is clear that the number of solutions will be $2$ since there are two intersecting points.
Hence, the correct answer is Option A.

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