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Show that if `f :R {(7)/(5)} to R - {(3)/(5)}` is defined by `f (x) = (3x +4)/( 5x -7) and g :R - {(3/(5)} to 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 TELUGU-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Show that if f :R {(7)/(5)} to R - {(3)/(5)} is defined by f (x) = (3x...

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  2. Let f : R to R be defined as f (x) =10 x +7. Find the function g : R t...

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

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

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  5. Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f...

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  6. Show that the function f: R to R given by f (x) = x ^(3) is injective...

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  7. Give examples of two functions f:N to Z and g: Z to Z such that g o f ...

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  8. Give examples of two functions f : N to N and g : N to N such g o f is...

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

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  10. Find the number of all onto functins from the set {1,2,3..,n} to itsel...

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  11. Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S...

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  12. Consider the binary opertions **: R xx R to R and o : R xx R to R defi...

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  13. Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as ...

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  14. If A = {0,1,2,3,4,5} Define a binary operation * on A as a*b = {{:(a+b...

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  15. Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defin...

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  16. Let A = {1,2,3}. Then number of relations containing (1,2) and (1,3) w...

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

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  18. Let f : R to R be the Signumb Function defined as f (x) = {{:(1",",...

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  19. Number of binary opertions on the set {a,b} are

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