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Prove that the function f: RR rarr RR d...

Prove that the function `f: RR rarr RR ` defined by, `f(x)=sin x`, for all `x in RR` is neither one -one nor onto.

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Let A be the set of quadrilaterals in a plane and RR^(+) be the set of positive real numbers. Prove that, the function f: A rarr RR ^(+) defined by f(x) = area of quadrilateral x, is * many-one and onto.

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

Let A be the set of triangles in a plane and RR^(+) be the set of positive real numbers. Then show that, the function f:A rarr RR^(+) defined by , f(x)= area of triangle x, is many -one and onto.

Let the function f: RR rarr RR be defined by, f(x)=x^(3)-6 , for all x in RR . Show that, f is bijective. Also find a formula that defines f ^(-1) (x) .

Let CC and RR be the sets of complex numbers and real numbers respectively . Show that, the mapping f:CC rarr RR defined by, f(z)=|z| , for all z in CC is niether injective nor surjective.

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CHHAYA PUBLICATION-MAPPING OR FUNCTION-EXERCISE 2A ( very short answer type questions)
  1. Let A={0,1}, B={2,6} and f: A rarr B be given by, f(x)=6-4x and g: A r...

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  2. Prove that the mapping f: RR rarr RR defined by ,f(x)=x^(2)+1 for all ...

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  3. Prove that the mapping f: RR rarr RR defined by ,f(x)=x^(2)+1 for all ...

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  4. Let A={-1,1,2,-3}, B={2,8,18,32} and f: A rarr B be defined by, f(x)=...

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  5. Prove that the function f: RR rarr RR defined by, f(x)=sin x, for all...

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  6. Show that the modulus function f: RR rarr RR , given by f(x)=|x| is n...

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  7. Show that, the mapping f:NN rarr NN defined by f(x)=3x is one-one but ...

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  8. Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bij...

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  9. Let A be a finite set If f: A rarr A is an onto mapping , show that it...

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  10. Let A be the set of quadrilaterals in a plane and RR^(+) be the set of...

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  11. Let A={-1,1,-2,2},B={3,4,5,6} and f: A rarr B be the mapping defined b...

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  12. Let D be the set of odd natural numbers . Then show that the mapping f...

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  13. Show that, the mapping f: RR rarr RR defined by f(x)=mx +n, where m,n...

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  14. Let A=RR-{2} and B=RR-{1}. Show that, the function f:A rarr B defined ...

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  15. Let CC be the set of complex numbers and f:CC rarr RR be defined by f(...

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  16. Show that the signum function f:RR rarr RR , given by f(x)={(1" if "...

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  17. Let A={x in RR :-1 le xle 1} =B. Show that, the mapping f:A rarr B de...

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  18. Let A={x in RR:-1 le x le 1} =B. Prove that , the mapping from A to B ...

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  19. Prove that , the mapping f:NN rarr NN defined by, f(x)={(x+1 " when...

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  20. Prove that the greatest integer function f: RR rarr RR, given by f(x)=...

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