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If A = (a,b,c,d) and f corresponds to th...

If A = (a,b,c,d) and f corresponds to the subset (a,b),(b,d),(c,a),(d,c) of the cartesian product `A xx A`. Show that f is a bijection and find `f^-1`

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Consider the function f : R - (-1) rarr R - (-1) defined by the rule f...

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  2. Write down the domain of the function f defined by f(x) = sqrt(25-x^2)

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  3. If A = (a,b,c,d) and f corresponds to the subset (a,b),(b,d),(c,a),(d,...

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  4. If g={(1,1),(2,3),(3,5),(4,7)} is a function described by the formula ...

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  5. Prove that: {:|(a^2,a,b+c),(b^2,b,c+a),(c^2,c,ab)| = -(a+b+c)(a-b)(b...

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  6. Let f : R rarr R be defined by f(x) = 1/x AA x inR, then f is

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

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  8. If f. g : R rarr R are defined respectively as f(X) = 2x + 1 and g (x)...

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  9. Are the following sets of ordered pairs functions? (x,y) : x is a pers...

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  10. Are the following sets of ordered pairs functions? (a,b), a is a pers...

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  11. If f(x) = x + 7 and g(x) = x - 7 , x in R find (fog) (7).

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  12. The range of function f(x)= abs(x-1)/(x-1)

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  13. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6...

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  14. If f(x) = x^2 and g (x) = 2x + 3, then the laue of gof (-1) is

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  15. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find fog

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  16. Let f(x) = x^2 and g (x) = sqrtx, then (fog) (x) = x for all x in D(fo...

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  17. Let '*' be the binary operation defined on N by the rule a * b = 3 a +...

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  18. Is the binary operation '*' defined on Z (set of integers) by the rule...

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  19. Let '*' be the operation defined on the set Z of integers by the rule ...

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  20. Let '*' be the binary operation defined on Q by the rule a * b = ab^2 ...

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