f-R-R-g-R-R-2f-x-f-x-1-g-x-1-g-x-2-f-x-1-g-x-1-f-1-1-g-1-2-f-0-g-0-

Question Number 1068 by 123456 last updated on 01/Jun/15

f : R \to R_{+}, g : R \to R_{+}

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

{[g (x)]}^{2} = f (x - 1) g (x + 1)

f (- 1) = 1, g (1) = 2, f (0) g (0) = ?

Answered by prakash jain last updated on 02/Jun/15

2 f (0) = f (- 1) g (1) = 2 \Rightarrow f (0) = 1

{[g (0)]}^{2} = f (- 1) g (1) = 2 \Rightarrow g (0) = \sqrt{2}

f (0) g (0) = \sqrt{2}

Commented by navajyoti.tamuli.tamuli@gmail. last updated on 13/Jun/15

2 f (0) = f (- 1) + g (1) = 3 => f (0) = \frac{3}{2}

{[g (0)]}^{2} = f (- 1) g (1) = 2 => g (0) = \sqrt{2}

f (0) g (0) = \frac{3}{\sqrt{2}}