if-f-x-x-x-2-then-f-1-x-

Question Number 206458 by mathlove last updated on 15/Apr/24

i f f (x) = \sqrt{x - x^{2}} t h e n f^{- 1} (x) = ?

Answered by Skabetix last updated on 15/Apr/24

f^{- 1} (x) = \frac{1 \pm \sqrt{- 4 x^{2} + 1}}{2}

Commented by Tinku Tara last updated on 15/Apr/24

If one value gives two result then f (x)

is not invertible

Commented by mathlove last updated on 15/Apr/24

y e s s i r

Answered by cortano21 last updated on 15/Apr/24

Answered by Frix last updated on 15/Apr/24

f (x) = \sqrt{x - x^{2}}

0 ⩽ x ⩽ 1 \land 0 ⩽ f (x) ⩽ \frac{1}{2}

\Rightarrow

f (x) = \sqrt{x - x^{2}}; 0 ⩽ x < \frac{1}{2}

f^{- 1} (x) = \frac{1}{2} - \frac{\sqrt{1 - 4 x^{2}}}{2}; 0 ⩽ x ⩽ \frac{1}{2}

f (x) = \sqrt{x - x^{2}}; \frac{1}{2} ⩽ x ⩽ 1

f^{- 1} (x) = \frac{1}{2} + \frac{\sqrt{1 - 4 x^{2}}}{2}; 0 ⩽ x ⩽ \frac{1}{2}

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