If-f-x-x-3-x-1-then-invrse-function-of-f-x-is-

Question Number 154725 by SLVR last updated on 21/Sep/21

I f f (x) = x^{3} + x + 1 t h e n i n v r s e f u n c t i o n

o f f (x) i s ? ? ?

Answered by mr W last updated on 21/Sep/21

y = x^{3} + x + 1

x^{3} + x + 1 - y = 0

x = \sqrt[3]{\sqrt{{(\frac{1}{3})}^{3} + {(\frac{1 - y}{2})}^{2}} - (\frac{1 - y}{2})} - \sqrt[3]{\sqrt{{(\frac{1}{3})}^{3} + {(\frac{1 - y}{2})}^{2}} + (\frac{1 - y}{2})}

x = \sqrt[3]{\sqrt{\frac{1}{27} + \frac{{(y - 1)}^{2}}{4}} + \frac{y - 1}{2}} - \sqrt[3]{\sqrt{\frac{1}{27} + \frac{{(y - 1)}^{2}}{4}} - \frac{y - 1}{2}}

\Rightarrow f^{- 1} (x) = \sqrt[3]{\sqrt{\frac{1}{27} + \frac{{(x - 1)}^{2}}{4}} + \frac{x - 1}{2}} - \sqrt[3]{\sqrt{\frac{1}{27} + \frac{{(x - 1)}^{2}}{4}} - \frac{x - 1}{2}}

Commented by SLVR last updated on 21/Sep/21

G r e a t \dots d e a r p r o f e s s o r \dots m r . W

I n e e d t o k n o w h o w x = i n 3 r d s t e p ?

k i n d l y \dots e x p l a i n

Commented by mr W last updated on 21/Sep/21

{C a r d a n o}^{'} s f o r m u l a f o r c u b i c e q u a t i o n .

s e e Q 89687

Commented by SLVR last updated on 21/Sep/21

T h a n k y o u \dots s i r \dots s o . . k i n d o f y o u

Facebook Tweet Pin