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If functions f : A rarr B and g : B rarr...

If functions `f : A rarr B and g : B rarr A` satisfy `gof = I_A` , then show that f is one one and g is onto.

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The correct Answer is:
Using theorem g is also one - one and onto .
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Let A = {a,b,c} and the relation R be defined on A as follows : R = {...

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  2. Let D be the domain of the real valued function f defined by f(x) = sq...

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  3. If f,g : R rarr R be defined by f(x) = 2x + 1 and g(x) =x^(2) -2 , AA...

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  4. Let f : R rarr R be the function defined by f(x) = 2x - 2 , AA x in R...

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  5. If A = {a,b,c,d} and the function f ={(a,b),(b,d) , (c,a) ,(d,c) } . W...

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  6. If f: R rarrR is defined by f(x) =x^(2)-3x+2 , find f(f(x)).

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  7. Is g= {(1, 1), (2,3), (3,5), (4,7)} a function, justify. If this is de...

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  8. Are the following set of ordered pairs functions ? If so examine wheth...

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  9. Are the following set of ordered pairs functions ? If so examine wheth...

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  10. If the mappings f and g are given be f = {(1,2),(3,5),(4,1)} and g = {...

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  11. Let C be the set of complex numbers . Prove that the mapping f : C rar...

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  12. Let the function f : R rarr R be defined by f(x) = cos x , AA x in R ...

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  13. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

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  14. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

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  15. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

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  16. Let X = {1,2,3} and Y = {4,5} . Find whether the following subsets of ...

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  17. If functions f : A rarr B and g : B rarr A satisfy gof = IA , then sho...

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  18. Let f : R rarr R be the function defined by f(x) = 1/(2-cosx),AA x in...

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  19. Let n be a fixed positive integer. Defiene a relation R in Z as follow...

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