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Let f= {(1,3),(2,4),(3,7)} and g ={(3,2)...

Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)}
Determine gof and fog if possible . Test whether fog =gof.

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Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determine gof and fog if possible. Test whether fog=gof.

Let A={1,2,3}, B={4,5,6,7} and let f={(1,4),(2,5),(3,6)} be a function from A to B. State whether f is one-one or not.

If A = {1, 2, 3), B = {4, 5, 6, 7) and f = {(1,4),(2,5), (3,6)} is a function from A to B.b State whether f is one-one or not.

If the mapping f and g are given by f= {(1,2), (3, 4), (5, 6), (7, 8)}, g={(2, 5),(4, 7),(6, 3),(8, 1)} then find (i) gof (ii) fog. Hence show that composition of functions is not commutative.

If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5), (3, 6)} is a function from A to B. State whether f is one-one or not.

If f(x)=sqrtx and g(x)=1-x^2 , then find gof and fog. If h(x)=1-x , then whether gof=h?

MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. Show that f : R to R defined as f(x) = sgn(x) is neither one-one nor o...

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  2. Give an example of a function which is injective but not surjective.

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  3. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  4. Express each of the following function as the sum of an even function ...

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  5. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  6. If the invertible function f is defined as f(X) = (3x-4)/5 , write f^(...

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  7. Let f , R to R and g , R to R defined as f(x) = | x |, g(x) = | 5x - 2...

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  8. Let * is a binary operation defined by a * b = 3a + 4b - 2, find 4*5.

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  9. Let the binary operation on Q defined as a * b = 2a + b - ab, find 3*4...

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  10. Let * is a binary operation on Z defined as a * b = a + b - 5 find the...

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  11. Find the number of binary operations on the set {a, b}.

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  12. Let * is a binary operation on [0, ¥) defined as a * b = sqrt (a^(2)+b...

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  13. List the members of the equivalence relation defined by {{1},{2},{3,4...

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  14. Find least non negative integer r such that 7xx13xx23xx413 -= r "(mod ...

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  15. Find least non negative integer r such that 1237"(mod 4)"+985"(mod 4)"...

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  16. For real numbers x and y, define x R y if and only if x-y +sqrt(2) is ...

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  17. Let A = {a,b,c) and the relation R be defined on A as follows: R={{a...

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  18. Let X and Y be sets containing m and n elements respectively.How many ...

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  19. Show that the relation R in the set of real numbers, defined as R = {(...

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  20. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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