f-x-x-3-3x-2-4x-1-find-a-whenever-f-a-f-1-a-

Question Number 155973 by Fareed last updated on 06/Oct/21

f (x) = x^{3} - {3 x}^{2} + 4 x - 1

find a = ?

whenever f (a) = f^{- 1} (a)

Commented by MJS_new last updated on 06/Oct/21

the graph of y = f^{- 1} (x) is the mirrored graph

of y = f (x) for any function . any intersection

of f (x) = f^{- 1} (x) is only possible oon the axis

of symmetry which is y = x .

y = f (x) \land y = x \Rightarrow x = f (x)

we {don}^{'} t need f^{- 1} (x)

Commented by Fareed last updated on 07/Oct/21

thanks

Answered by mr W last updated on 06/Oct/21

x^{3} - {3 x}^{2} + 4 x - 1 = x

x^{3} - {3 x}^{2} + 3 x - 1 = 0

{(x - 1)}^{3} = 0

\Rightarrow x = 1 = a

i . e . f (1) = f^{- 1} (1)

Commented by Fareed last updated on 06/Oct/21

can you explian a little more pleae

Commented by Fareed last updated on 06/Oct/21

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

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