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Show that an onto function f : {1, 2, 3}...

Show that an onto function `f : {1, 2, 3} ->{1, 2, 3}`is always one-one.

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`{1,2,3}`
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Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one-one.

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Show that the function f:N rarr N , given by f(x) = 2x, is one-one but not onto.

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Let f: {1, 2, 3} rarr {a,b,c} be one-one and onto function given by f(1) = a, f(2) = b and f(3) = C. Show that there exists a function g: {a,b,c} rarr {1,2,3} such that gof =I_(x) and fog = I_Y , where X = {1,2,3} and Y = {a,b,c} ,

Prove that the function f :R rarr R , given by f(x) = 2x, is one-one and onto.

Find the number of all one-one functions from set A = {1, 2, 3} to itself.

Show that the function f: R rarr R , defined as f(x) = x^2 , is neither one-one nor onto.

Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) =x/(1+|x|),x in R is one one and onto function.

The number of onto function from set {1,2,3,4} " to " {3,4,7} is .......

NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Show that an onto function f : {1, 2, 3} ->{1, 2, 3}is always one-one...

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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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