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Change of Variables

if f(x) = x+3...

Question

if f(x) = x+3 / x+2 , prove that x= (2f(x) - 3) / (1-f(x))

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f (x) = x + \frac{1}{x}

[f (x)]^{3} = f (x^{3}) + 3 f (\frac{1}{x})

f (x) = \frac{(x - 1)}{(x + 1)}

then prove that

f (2 x) = \frac{3 f (x) + 1}{f (x) + 3}

Q. If a function such that

f (0) = 2; f (1) = 3

f (x + 2) = 2 f (x) - f (x + 1) \forall x \in R

f (x) = \frac{x + 2}{2 x + 3}

\int {(\frac{f (x)}{x^{2}})}^{1 / 2} d x = \frac{1}{\sqrt{2}} g (\frac{1 + \sqrt{2 f (x)}}{1 - \sqrt{2 f (x)}}) - \sqrt{\frac{2}{3}} h (\frac{\sqrt{3 f (x)} + \sqrt{2}}{\sqrt{3 f (x)} - \sqrt{2}}) + c

f (x)

is a function such that

f (0) = 2, f (1) = 3

f (x + 2) = 2 f (x) - f (x + 1)

\forall x \in R

f (5)

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