If f ( x ) = sin {[ x + 5 ] + { x − { x }}} for x ∈ ( 0 , 4 π ) is invertible, where \{.\} and [.] represent fractional part and greatest integer functions respectively, then f − 1 ( x ) is

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If f ( x ) = sin {[ x + 5 ] + { x − { x }}} for x ∈ ( 0 , 4 π ​ ) is invertible, where \{.\} and [.] represent fractional part and greatest integer functions respectively, then f − 1 ( x ) is

TestHub · Accepted Answer

y = f ( x ) = sin {[ x + 5 ] + { x − { x − { x }}}} = sin { x − { x − { x }}} = sin { x − {[ x ]}} = sin { x − 0 } = sin { x } = sin x Since 0 < x < 4 π ​ , we have x = sin − 1 y or f − 1 ( x ) = sin − 1 x .

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