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

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

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

Let f:{1,2,3} to {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} to {1,2,3} such that gof =I _(x) and fog =I _(y), where, X = {1,2,3} and Y={a,b,c}.

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

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

If x>1/2 , show that the function f(x) = x(4x^2 - 3) is steadily increasing.

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

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

Let f(x) and g(x) be one-one onto functions where f : {a,b,c,d} rarr {1,2,3,4} and g : {3,4,5,6} rarr {w,x,y,z} respectively. The number of elements in the range set of g (f(x)) are

If x gt 1/2 , show that the function f(x) =x(4x^(2)-3) is steadily increasing.

Let RR be the set of real numbers and A=R-{3},B=R-{1} . Show that , f: A rarr B defined by , f(x) =(x-1)/(x-3) is a one-one onto function.

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

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

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

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

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  13. Show that +:R×R→R and o:R×R→R defined as a∗b=∣a−b∣ and aob=a for all a...

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

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  15. Define a binary opertion ** on the set {0,1,2,3,4,5} as a**b ={{:(a+...

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

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

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  18. Let A = {1,2,3},B={5,6.7} then find AcapB

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  19. Let f: R → R be the Signum Function defined as f(x)={ 1, x>0 0, x=0−1,...

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

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