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Show that a one-one function f : {1, 2, ...

Show that a one-one function `f : {1, 2, 3} rarr {1, 2, 3}` must be onto.

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Explore conceptually related problems

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

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} ,

Let f be a one-one function with domain {x,y,z} and range {1,2,3} . It is given that exactly one of the following statements is true and the remaining two are false f(X)=1, f(y)!=1 f(z)!=2 determine f^(-1)(1)

Show that the function f : R rarr R , defined by f(x) =1/x is one - one and onto , where R is the set of all non - zero real number . is the result true, if the domain R is replaced by N with co-domain being same as R ?

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

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

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.

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

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1...

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

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  3. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be ont...

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  4. Let f: {2, 3, 4, 5} rarr {3, 4, 5, 9} and g : {3, 4, 5, 9} rarr {7, 1...

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  5. Find gof and fog, if f:R rarr R and g: R rarrR are given by f(x) = c...

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  6. Show that if f: R - {7/5} rarr R - {3/5} is defined by f(x) = (3x+4)/...

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  7. Show that if f: A rarr B and g: B rarr C are one- one, then gof: A ra...

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  8. Show that if f: A rarr B and g: B rarr C are onto, then gof: A rarr ...

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  9. Consider functions f and g such that composite gof is defined and is o...

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  10. Are fand g both necessarily onto, if gof is onto?

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  11. Let f: {1, 2, 3} rarr {a,b,c} be one-one and onto function given by f...

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  12. Let f:N rarr Y be a function defined as f(x) = 4x + 3, where, Y = { y...

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  13. Let Y = {n^(2) :n in N} subN Consider f: N rarr Y as f(n) = n^2 . Sh...

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  14. Let f':N rarr R be a function defined as f'(x) = 4x^(2) + 12x + 15 . ...

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  15. Consider f: N rarr N,g :N rarr N and h: Nrarr R defined as f(x) = 2x, ...

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  16. Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} de...

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  17. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  18. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  19. Let S = {1, 2, 3}. Determine whether the functions f:S rarr S defined ...

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  20. Show that addition, subtraction and multiplication are binary operatio...

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