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Let A be a non - empty set such that A x...

Let `A` be a non - empty set such that `A xx B=A xx C` show that `B=C`

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTIONBANK
  1. If f is a real function defined by f(x)=(x-1)/(x+1), then prove that f...

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  2. Find the domain and range of the following functions: i)f(x)=1/(sqrt(x...

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  3. Let f and g be two real functions defined by f(x)=1/(x+4) and g(x)=(x+...

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  4. Which of the following relations are functions? Give reasons. If it is...

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  5. If f(x)=x^2+x-1 and g(x)=4 x-7. be real functions then find: i) (f+g)...

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  6. Let f and g be real functions defined by f(x)=sqrt(x+4), x ge-4 and g(...

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  7. If af(x)+bf (1/x)=1/x-5 for x ne 0, where a ne b. Find f(x)

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  8. If A={3,4,6} , B={1,3} and C={1,2,6}, then find (i) A xx(B nn C) (...

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  9. Let A and B are two sets such that n (A) = 3 and n (B) = 2. If (x,1),...

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  10. Let A be a non - empty set such that A xx B=A xx C show that B=C

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  11. Let A subset B, C subset D, then prove that A xx C subset B xx D

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  12. Let R be the relation on Z defined by R={(a, b), a, b in Z, a^2=b^2} F...

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  13. Let R be the relation on Z defined by R = { ( a,b): a,b in Z, a - b i...

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

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  15. If f(x)=x+1/x show that (f(x))^3=f(x^3)+3 f(x)

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  16. Find the domain of the following. f(x)=(x^2+2x+1)/(x^2-8x+12)

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  17. Draw the graph of the real function y=x^2+2 x+3

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  18. Draw the graph of the real function y={[ x, if x le 0], [ x^2, if...

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  19. Let f: R rarr R be a function defined by f(x)=x^2+[x]+|x|-7, x in R. F...

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  20. Let f, g: R rarr R be functions defined respectively by f(x)=x+1, g(x)...

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