If f(x) satisfies the relation f((5x-3y)...

If `f(x)` satisfies the relation `f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in R ,` and `f(0)=3a n df^(prime)(0)=2,` then the period of `"sin"(f(x))` is `2pi` (b) `pi` (c) `3pi` (d) `4pi`

A

`2pi`

B

`pi`

C

`3pi`

D

`4pi`

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AI Generated Solution

To solve the problem step by step, we will analyze the given functional equation and the conditions provided. ### Step 1: Analyze the functional equation We have the relation: \[ f\left(\frac{5x - 3y}{2}\right) = \frac{5f(x) - 3f(y)}{2} \] This resembles the form of a linear function. ...

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