find-f-x-such-that-f-x-f-1-x-

Question Number 173624 by mr W last updated on 15/Jul/22

f i n d f (x) s u c h t h a t f^{'} (x) = f^{- 1} (x) .

Commented by infinityaction last updated on 15/Jul/22

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

f {f^{'} (x)} = x, f (x) = {a x}^{b}

f (a b x^{b - 1}) = x

a \cdot a^{b} b^{b} \cdot x^{b^{2} - b} = x

x^{\underset{0}{\underset{⏟}{b^{2} - b - 1}}} = \frac{1}{\underset{1}{\underset{⏟}{a \cdot a^{b} b^{b}}}}

b = \frac{1 \pm \sqrt{5}}{2} = ϕ t h e n a =^{ϕ} \sqrt{\frac{1}{ϕ}}

f (x) =^{ϕ} \sqrt{\frac{1}{ϕ}} x^{ϕ}

Commented by mr W last updated on 15/Jul/22

y e s . a n y o t h e r p o s s i b i l i t i e s ?

Commented by infinityaction last updated on 15/Jul/22

i t h i n k n o b u t i a m n o t s u r e

Commented by infinityaction last updated on 15/Jul/22

s o r r y s i r i {d o n}^{'} t g e t i t

Commented by infinityaction last updated on 15/Jul/22

o k e y

Commented by Tawa11 last updated on 15/Jul/22

Great sirs

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