If-f-2-R-f-x-x-2-1-1-x-2-f-1-pi-

Question Number 184938 by mnjuly1970 last updated on 14/Jan/23

If, {\begin{cases} f : [\sqrt{2}, + \infty) \to R \\ f (x) = x^{2} + ⌊ \frac{1}{1 - ⌊ x^{2} ⌋} ⌋ \end{cases}

\Rightarrow ⌊ f^{- 1} (π) ⌋ = ?

Answered by Frix last updated on 14/Jan/23

\sqrt{π + 1}

Commented by mnjuly1970 last updated on 14/Jan/23

t h a n k s a l o t \dots

Commented by Frix last updated on 14/Jan/23

Sorry for the missing solution, {it}^{'} s just the

result of my playing around with it

Answered by mnjuly1970 last updated on 14/Jan/23

m y s o l u t i o n :

x ⩾ \sqrt{2} \Rightarrow x^{2} ⩾ 2 \Rightarrow ⌊ x^{2} ⌋ ⩾ 2

\Rightarrow 1 - ⌊ x^{2} ⌋ ⩽ - 1 < 0

\Rightarrow 0 > \frac{1}{1 - ⌊ x^{2} ⌋} ⩾ - 1

f (x) = x^{2} - 1

f^{- 1} (x) = \sqrt{x + 1}

⌊ f^{- 1} (π) ⌋ = ⌊ \sqrt{π + 1} ⌋ = 2

Commented by aba last updated on 14/Jan/23

good

Commented by Mastermind last updated on 15/Jan/23

Is this a solution to my question

pls, could you please make it easier

than this ?