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Show that the inverse of a bijective is ...

Show that the inverse of a bijective is also a bijection.

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Show that the inverse of a bijective function is unique.

What is inversion ?

Let f:XrightarrowY and g:YrightarrowZ . Prove that gof is bijective if both f and g are bijective. Also prove that (gof)^(-1)=f^(-1)og^(-1) .

Let f be defined by f(x)=4x + 3 for all x""inR. Show that it is bijective and determine the inverse of f.

Consider f:R -{-(4)/(3)} to R -{(4)/(3)} given by f(x) =(4x+3)/(3x+4) . Show that f is bijective. Find the inverse of f and hence find f^(-1)(0) and x such that f^(-1)(x)=2 .

Let f be defined by f (x)=2x + 1 for all xinR . Show that f is bijective and determine the inverse of f. Find f^(-1)(0),f^(-1)(2) and f^(-1)(-1) .

Give an example of a function which is bijective

SHARAM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE
  1. If ff(x)=cos[pi^2]x+cos[-pi^2]x where [x] stands for the greatest inte...

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  2. If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...

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  3. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

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  4. Prove that the relation R on the set Z of all integers defined by R={(...

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  5. Let n be positive integer and a function f be defined as f(n)={(0 , wh...

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  6. If f:RrarrR defined by f(x)=5x-8 for all x inR, then show that f is in...

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  7. Show that the inverse of a bijective function is unique.

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  8. Show that the inverse of a bijective is also a bijection.

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  9. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

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  10. Prove that the greatest integer function f:R rarr R, given by f(x) = [...

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  11. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

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  12. Show that the fuction f:RrarrR defined by f (x)=sin x is neither one-...

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  13. If f:N to N is defined by. f(n)={((n+1)/(2)", if n is odd"),((n)/(2)...

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  14. Show that a fuction f:RrarrR given by f(x)=ax+b, a, bin R and a!=0 is ...

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  15. Let* be a binary operation on Q, defined by a*b=(3ab)/(5) .Show that i...

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  16. If A=N xx N and * is a binary operation on A defined by (a, b) ** (c,...

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  17. A binary operation * on the set {0,1,2,3,4,5} is defined as a*b= {{...

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  18. Let us consider a binary operation ** on the set {1, 2, 3, 4, 5} given...

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  19. Let us consider a binary operation ** on the set {1, 2, 3, 4, 5} given...

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  20. Let us consider a binary operation ** on the set {1, 2, 3, 4, 5} given...

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