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Graph of Fractional Part Function

The number of...

Question

The number of solutions of the equation $[x] + 2 {- 3} = 3 x$ is (where [ ] represents the greatest integer function and {x} denotes the fractional part of x)

1

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2

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3

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0

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Solution

The correct option is D $2$
Fractional part of integers is 0.

Hence effectively equation is

$[x] = 3 x$

which has the following $2$ solutions

$x = - \frac{1}{3}, x = 0$

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