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De Morgan's Law

If a function...

Question

If a function for is bijective then what can we say about its inverse

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Solution

Dear student

$\mapsto I f t h e f u n t i o n i s b i j e c t i v e, t h e n i t s i n v e r s e i s u n i q u e a n d b i j e c t i v e . \mapsto L e t f : A \to B b e f u n c t i o n s u c h t h a t f i s b i j e c t i v e a n d g : B \to A i s i n v e r s e o f f . T h e n f o g = I_{B} = i n d e n t i t y e l e m e n t o f s e t B a n d g o f = I_{A} = i n d e n t i t y e l e m e n t o f s e t A$
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Similar questions

f : A \to B

be a function defined by

y = f (x)

where f is a bijective function, means f is injective (one-one) as well as surjective (onto), then there exist a unique mapping

g : B \to A

f (x) = y

g (y) = x \forall x ϵ A, y ϵ B

Then function g is said to be inverse of f and vice versa so we write

g = f^{- 1} : B \to A [{f (x), x} : {x, f (x)} ϵ f^{- 1}]

when branch of an inverse function is not given (define) then we consider its principal value branch.

Which of the following is not correct?

Q. Choose the correct option regarding the following statements.
(i) If R is an equivalence relation, then

R^{- 1}

is also an equivalence
(ii) Inverse of a bijective function is unique
(iii) Even function can be one-one
(iv) Constant functions are aperiodic

f : A \to B

be a function defined by

y = f (x)

where f is a bijective function, means f is injective (one-one) as well as surjective (onto), then there exist a unique mapping

g : B \to A

f (x) = y

g (y) = x \forall x ϵ A, y ϵ B

Then function g is said to be inverse of f and vice versa so we write

g = f^{- 1} : B \to A [{f (x), x} : {x, f (x)} ϵ f^{- 1}]

when branch of an inverse function is not given (define) then we consider its principal value branch.

- 1 < x < 0

{tan}^{- 1} x

f : A \to B

be a function defined by

y = f (x)

where f is a bijective function, means f is injective (one-one) as well as surjective (onto), then there exist a unique mapping

g : B \to A

f (x) = y

g (y) = x \forall x ϵ A, y ϵ B

Then function g is said to be inverse of f and vice versa so we write

g = f^{- 1} : B \to A [{f (x), x} : {x, f (x)} ϵ f^{- 1}]

when branch of an inverse function is not given (define) then we consider its principal value branch.

x < 0

{tan}^{- 1} x + {tan}^{- 1} \frac{1}{x}

Q. Instead of subtracting 32570 from a number. If 23570 is subtracted. Then what can we say about the answer?

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