ফাংশনের মান নির্ণয়

Let a function f(x)f(x) satisfies f2(x)f2(y)=4(xy)f^{2}(x)-f^{2}(y)=4(x-y) and f(0)=2(f(x)0)f(0)= 2\left ( f\left ( x \right )\geq 0 \right )whose domain is [a,)\left [ a ,\infty \right ) and it is differentiable on (a,)\left (a ,\infty \right )

The value of f(3)f(3) is

কাজু বাদাম

f2(x)f2(y)=4(xy)f^{2}(x)-f^{2}(y)=4(x-y)

and f(0)=2(f(x)0)f(0)= 2\left ( f\left ( x \right )\geq 0 \right )

f2(x)f2(y)=4(xy)f^{2}(x)-f^{2}(y)=4(x-y)

Put y=0,

f2(x)f2(0)=4xf^{2}(x)-f^{2}(0)=4x

f2(x)=4x+4f^{2}(x)=4x+4

f2(3)=16f^{2}(3)=16

f(x)=±4f(x) = \pm 4

But given f(x)0f(x) \ge 0,

Hencef(3)=4f(3)=4

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