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Let A={a ,\ b ,\ c} , B={u\ v ,\ w} and ...

Let `A={a ,\ b ,\ c}` , `B={u\ v ,\ w}` and let `f` and `g` be two functions from `A` to `B` and from `B` to `A` respectively defined as: `f={(a ,\ v),` `(b ,\ u),\ (c ,\ w)}` , `g={(u ,\ b),\ (v ,\ a),\ (w ,\ c)}dot` Show that `f` and `g` both are bijections and find `fog` and `gofdot`

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RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and g={(1,\ 3),\ (3,\ 3),\ (4,\ ...

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  2. Let f={(1,-1),(4,-2),(9,-3),(16 ,4)} and g={(-1,-2),(-2 ,-4),(-3,-6),(...

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  3. Let A={a ,\ b ,\ c} , B={u\ v ,\ w} and let f and g be two functions f...

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  4. Find fog\ (2) and gof\ (1) when: f: R->R ; f(x)=x^2+8 and g: R->R ; g(...

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  5. Let R^+ be the set of all non-negative real numbers. If f: R^+\ ->R...

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  6. Let f: R->R and g: R->R be defined by f(x)=x^2 and g(x)=x+1 . Show tha...

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  7. Let f: R->R and g: R->R be defined by f(x)=x+1 and g(x)=x-1. Show th...

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  8. Verify assoiativity for the following three mappings : f: NvecZ0...

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  9. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

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  10. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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  11. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  12. If f: A->B and g: B->C are one-one functions, show that gof is one-o...

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  13. If f: A->B and g: B->C are onto functions, show that gof is an onto fu...

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  14. If f: R->R and g: R->R be functions defined by f(x)=x^2+1 and g(x)=sin...

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  15. If f:[0,oo)->R and g: R->R be defined as f(x)=sqrt(x) and g(x)=-x^2-1,...

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  16. If f(x)=e^x and g(x)=(log)e x(x >0), find fog and gof. Is fog=gof?

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  17. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

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  18. If f(x)=1/x and g(x)=0 are two real functions, show that fog is not...

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  19. Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

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  20. Let f(x)=[x] and g(x)=|x| . Find (gof)(5/3) fog(5/3)

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