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Give an example of a map Which is neit...

Give an example of a map
Which is neither one - one nor onto.

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The correct Answer is:
f is not onto function
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Give an example of a map Which is not one - one but onto

Give an example of a map Which is one - one but not onto

Let C and R denote the set of all complex numbers and all real numbers respectively. Then show that f: C->R given by f(z)=|z| for all z in C is neither one-one nor onto.

Let C be the set of complex numbers . Prove that the mapping f : C rarr R given by f(z) = |z| , AA z in C , is neither one - one nor onto .

Give an example of relation . Which is Transitive but neither reflexive nor symmetric .

Prove that the Greatest Integer Function f : R rarr R , given by f(x) = [x] , is neither one - one nor onto , where [x] denotes the greatest integer less than or equal to x.

Show that the Signum Function f : R rarr R given by f(x) = {(1," if " x gt0),(0," if " x =0),(-1," if " x lt0):} is neither one - one nor onto.

Give an example of relation . Which is Symmetric but neither reflexive nor transitive.

Let the function f : R rarr R be defined by f(x) = cos x , AA x in R . Show that f is nether one - one nor onto .

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

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Solutions of NCERT Exemplar Problems (Long Answer Type Questions)
  1. Give an example of a map Which is one - one but not onto

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  2. Give an example of a map Which is not one - one but onto

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  3. Give an example of a map Which is neither one - one nor onto.

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  4. Let A = R - {3} , B = R - {1} . If f : A rarr B be defined f(x) = (x-2...

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  5. Let A = [-1,1] . Then , discuss whether the following functions define...

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  6. Let A = [-1,1] . Then , discuss whether the following functions define...

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  7. Check the injectivity and surjectivity of the following function . f...

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  8. Let A = [-1,1] . Then , discuss whether the following functions define...

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  9. Each of the following defines a relation of N : x is greater than y...

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  10. Each of the following defines a relation of N : x+y = 10 , x , y in ...

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  11. Each of the following defines a relation of N : x. y is square of a...

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  12. Each of the following defines a relation of N : x+4y =10 , x , y in ...

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  13. Let A = {1,2,3.......9} and R be the relation in AxxA defined by (a,b)...

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  14. Using the definition ,prove that the function F : AtoB is invertible ...

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  15. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  16. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  17. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  18. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

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  19. Let ** be the binary operation defined on Q. Find which of the follow...

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  20. Let ** be the binary operation defined on Q. Find which of the follow...

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