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Let `f: RvecR` and `g: vecR` be two functions such that `fog(x)=sinx^2a n dgof(x)=sin^2xdot` Then, find `f(x)a n dg(x)dot`

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Given:
`f:R->R`
`g:R->R`
`fog(x)=f{g(x)}=sinx^2`
`Also, gof=g{f(x)}=sin^2x`
`g(x)=x^2`
`f(x)=sinx`
`gof(x)=(sin x)^2`
...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Let f: R->R be the signum function defined as f(x)={1,\ x >0,\ \ \ \ 0...

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  2. Let A={x in R :0lt=xlt=1}dot If f: AvecA is defined by f(x)={x ,ifx Q...

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  3. Let f: RvecR and g: vecR be two functions such that fog(x)=sinx^2a n...

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  4. If f: R->R be given by f(x)=sin^2x+sin^2(x+pi//3)+cosx\ cos(x+pi//3) f...

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  5. Let f: ZvecZ be defined by f(n)=3n for all n in Z and g: Zvec be defi...

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  6. Let f: RvecR be a function given by f(x)=a x+b for all x in R . Find ...

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  7. Let f: A->A be a function such that fof=f . Show that f is onto if and...

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  8. Let f,g: RvecR be two functions defined as f(x)=|x|+x and g(x)=|x|-x ,...

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  9. Find gof and gof when f: R->R and g: R->R is defined by f(x)=2x+3 and ...

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  10. Find gof and gof when f: R->R and g: R->R is defined by f(x)=2x+x^2 an...

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  11. Find fog(2) and gof(1) when: f: R rarr R ;f(x)=x^2+8 and g: R rarr ...

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  12. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x and g(x...

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  13. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x^2+2x-3 ...

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  14. Find gof and gof when f: R->R and g: R->R is defined by f(x)=8x^3 and ...

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  15. Let f={(3,\ 1),\ (9,\ 3),\ (12 ,\ 4)} and ={(1,\ 3),\ (3,\ 3),\ (4,\ 9...

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  16. Let f={(1,-1),(4,-2),(9,-3),(16 ,4)} and g={(-1,-2),(02 ,-4),(-3,-6),(...

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

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

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

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  20. 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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