nice-mathematics-if-f-x-x-3-x-then-find-f-1-x-

Question Number 123987 by mnjuly1970 last updated on 29/Nov/20

\dots n i c e m a t h e m a t i c s \dots

i f f (x) = x^{3} + x t h e n

f i n d f^{- 1} (x) = ?

Answered by MJS_new last updated on 29/Nov/20

y^{3} + y - x = 0

D = \frac{1}{27} + \frac{x^{2}}{4} > 0 \forall x \in R

\Rightarrow

f^{- 1} (x) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3 (27 x^{2} + 4)}}{18}} - \sqrt[3]{- \frac{x}{2} + \frac{\sqrt{3 (27 x^{2} + 4)}}{18}}

Commented by john_santu last updated on 30/Nov/20

C a r d a n o

Commented by MJS_new last updated on 30/Nov/20

yes

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