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Show that if f: R-{7/5}->R-{3/5} is d...

Show that if `f: R-{7/5}->R-{3/5}` is defined by `f(x)=(3x+4)/(5x-7)` and `g: R-{3/5}->R-{7/5}` is define by `g(x)=(7x+4)/(5x-3)` , then `fog=I_A` and `gof=I_B` , where `A=R-{3/5}, B=R-{7/5}; I_A(x)=x ,AAx in A , I_B(x)=x ,AAx in B` are called ide

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Show that if f: R - {7/5} rarr R - {3/5} is defined by f(x) = (3x+4)/(5x-7) and g: R - {3/5} rarr R - {7/5} is defined by g(x) = (7x +4)/(5x-3) , then fog =I_A and gof = I_(B) , where A = R - {3/5} , B = R - {7/5} , I_(A) (x) = x, AA x in A , I_(B) (x) = x, AA x in B are called identity functions on sets A and B , respectively .

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NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Show that if f: R-{7/5}->R-{3/5} is defined by f(x)=(3x+4)/(5x-7) a...

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  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

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  3. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

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  4. If f:R to R is defined by f(x) = x^(2)-3x+2, write f{f(x)}.

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  5. Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...

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  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

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  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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  9. Given a non-empty set X , consider P\ (X) which is the set of all subj...

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  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

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  11. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

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  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

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  13. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

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  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

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  15. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

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  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

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  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

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  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

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  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

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  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

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