Let f ( x ) = x sin 2 π x x 3 1 2 x 2 3 x 4 1 1 1 . If f ( x ) is an odd function and its odd values are equal to g ( x ) , then find the value of λ . If λ f ( 1 ) g ( 1 ) = 4 .

Question

Let f ( x ) = ​ x sin 2 π x x 3 ​ 1 2 x 2 3 x 4 ​ 1 1 1 ​ ​ . If f ( x ) is an odd function and its odd values are equal to g ( x ) , then find the value of λ . If λ f ( 1 ) g ( 1 ) = 4 .

TestHub · Accepted Answer

f ( − x ) = − f ( x ) = g ( x ) ∴ f ( x ) ⋅ g ( x ) = − ( f ( x ) ) 2 or f ( 1 ) g ( 1 ) = − ( f ( 1 ) ) 2 = − ​ 1 0 1 ​ 1 2 3 ​ 1 1 1 ​ ​ = − 4 ⇒ λ = 1 Ans.

Mathematics - Determinant Question with Solution | TestHub

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