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Differentiation of a Determinant

Let f be a fu...

Question

Let f be a function such that f(3)= 1 and f(3x) = x+ f(3x - 3) for all x. Then find the value of f(300).

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Solution

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f (3) = 1

f (3 x) = x + f (3 x - 3)

x

f (300)

f (3 x) = f^{'} (x) \cdot f^{''} (x)

x \in R

f

n

f (3 x) = f^{'} (x) f^{''} (x),

x \in R .

f

f

x \to 2 x^{2} + 3

f (3)

x \in R - {0, 1},

f_{1} (x) = \frac{1}{x}

f_{2} (x) = 1 - x

f_{3} (x) = \frac{1}{1 - x}

J (x)

(f_{2} \circ J \circ f_{1}) (x) = f_{3} (x)

J (x)

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