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Let R be the set of real numbers. If ...

Let `R` be the set of real numbers. If `f: R->R :f(x)=x^2` and `g: R->R ;g(x)=2x+1.` Then, find `fog` and `gof` . Also, show that `fog!=gofdot`

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Given that,
`f(x)=2x+1`and `g(x)=x^2, `for all` x in R`
Then,
`(gof)x=g(f(x))`
=`g(2x+1)`
=`(2x+1)^2`
=`4x^2+4x+1`
...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Show that f: R->R , given by f(x)=x-[x] , is neither one-one nor onto.

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  2. Let f: N->N be defined by: f(n)={n+1,\ if\ n\ i s\ od d n-1,\ if\ n\ i...

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  3. Let R be the set of real numbers. If f: R->R :f(x)=x^2 and g: R->R ...

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  4. Let : R->R ; f(x)=sinx and g: R->R ; g(x)=x^2 find fog and gof .

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  5. Let f:{2,3,4,5}vec{3,4,5,9}a n dg:{3,4,5,9}vec{7, 11 , 15} be function...

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  6. Let f:{1,\ 3,4\ }->{1,\ 2,\ 5} and g:{1,\ 2,\ 5}->{1,\ 3} be given by ...

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  7. Find gof and fog , if f: R->R and g: R->R are given by f(x)=|x| and g(...

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  8. If the functions f and g are given by f={(1,\ 2),\ (3,\ 5),\ (4,\ 1)} ...

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  9. If the function f: R->R be given by f(x)=x^2+2 and g: R->R be given by...

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  10. If f: R-{7/5}->R-{3/5} be defined as f(x)=(3x+4)/(5x-7) and g: R-{3/5}...

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  11. If f: R ->Ris defined by f(x) = x^2- 3x + 2, find f(f(x)).

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  12. If f,g: RvecR are defined respectively by f(x)=x^2+3x+1,g(x)=2x-3, fin...

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  13. Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=IZ .

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  14. If f: Z->Z be defined by f(x)=2x for all x in Z . Find g: Z->Z such t...

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  15. Let f,\ g and h be functions from R to R . Show that (f+g)oh=foh+goh

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  16. Let f,\ g and h be functions from R to R . Show that (fg)oh=(foh)(goh)

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  17. Let f: R->R be the signum function defined as f(x)={1,\ x >0,\ \ \ \ 0...

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

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

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  20. 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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