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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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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.

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.

Show that the function f (x) = {{:( x, if x lt 1), ( 6 -2x , if 1 le x le 3), ( x ^(2) - 4x + 3, if x gt 3):} is not differentiable at x = 1,3

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

Show that the Modulus Functions f : R to R, given by f (x) =|x|, is neither one-one nor onto, whre |x| is x, if x is positive or 0 and |x| is -x, if x is negative.

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NCERT TELUGU-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. 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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