If f(x) satisfies the relation fleft( {f | vedclass

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Question

Given $f\left(\frac{5 x-3 y}{5-3}\right)=\frac{5 f(x)-3 f(y)}{5-3}$

Which satisfies section formula for abscissa on

$L.H.S.$ and ordinate on $R.

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

Given $f\left(\frac{5 x-3 y}{5-3}\right)=\frac{5 f(x)-3 f(y)}{5-3}$

Which satisfies section formula for abscissa on

$L.H.S.$ and ordinate on $R.H.S.$

Hence $f(x)$ must be linear function

let $f(x)=a x+b$

$f(0)=b=1 \Rightarrow f(x)=2 x+1$

$f(0)=a=2$

period of $\sin (2 \mathrm{x}+1)$ is $\pi$

If $f(x)$ satisfies the relation $f\left( {\frac{{5x - 3y}}{2}} \right)\, = \,\frac{{5f(x) - 3f(y)}}{2}\,\forall x,y\in R$ $f(0) = 1, f '(0) = 2$ then period of $sin \ (f(x))$ is

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