Find the domain of f x - - - x - - 1 - - 4 - - x -where - - represents the greatest integer function-

[ [ x ] 1 ≥ 0; 4 [ x ] ≥ 0; #160;= 1 ≤[ x ] ≤ 4; #160;= 1 ≤ x lt; 5; x ∈( 1,5) ] ...

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Real Valued Functions

Find the doma...

Question

Find the domain of
$f (x) = \sqrt{([x] - 1)} + \sqrt{(4 - [x])}$
(where [ ] represents the greatest integer function).

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Solution

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f (x) = \sqrt{([x] - 1)} + \sqrt{(4 - [x])}

f (x) = \frac{1}{\sqrt{[x]^{2} - [x] - 6}}

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f (x) = \sqrt{[x] - 1}

f (x) = {log}_{[x + \frac{1}{2}]} | x^{2} - x - 2 |

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f (x) = \sqrt{\frac{[x] - 2}{5 - [x]}},

[.]

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