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Let Q be the set of all rational number ...

Let Q be the set of all rational number in `[0, 1]` and `f:[0, 1]rarr[0, 1]` be defined by `f(x)={{:(x," for ", x in Q),(1-x," for ", x cancel(in)Q):}` Then the set `S={x in [0, 1] (fof)(x)=x}` is equal to

A

Q

B

`[0, 1]-Q`

C

`(0, 1)`

D

`[0, 1]`

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DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
  1. If f:RR rarrRR and g:RR rarrRR are defined by f(x)=2x+3 and g(x)=x^(2)...

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  2. Suppose f:[-2, 2] rarr RR is defined by f(x)={{:(-1" for "-2 le x le 0...

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  3. Let Q be the set of all rational number in [0, 1] and f:[0, 1]rarr[0, ...

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  4. If f : R rarr R and g: R rarr R are given by f(x)=|x| and g(x)={x} for...

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  5. If g[f(x)]=|sinx|, f[g(x)]=(sinsqrtx)^(2) then

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  6. If g[f(x)]=|sinx|, f[g(x)]=(sinsqrtx)^(2) then

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  7. If f(n)=(-1)^(n-1)(n-1) and g(n)=n-f (n)AA n in N then (gog)(n)=

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  8. If f(x) =(p-x^n)^(1/n) ,p >0 and n is a positive integer then f[f(x)] ...

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  9. If f(x)=(25-x^(4))^(1//4) for 0 lt x lt sqrt5 then f(f((1)/(2)))=

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  10. If f:[-6, 6]rarr RR defined by f(x)=x^(2)-3" for " x in R then (fofof...

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  11. If f(x)=(1)/(sqrt(x+2sqrt(2x-4)))+(1)/(sqrt(x-2sqrt(2x-4))) for x gt 2...

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  12. If f(x)=sin^(2)x+sin^(2)(x+pi//3)+cosxcos(x+pi//3) and g(5//4)=1 then ...

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  13. If f(x)=cos^(2)x+cos^(2)(x+60^(@))+cos^(2)(x-60^(@)) and g(3//2)=5 the...

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  14. If y=f(x)=(2x-1)/(x-2), then f(y)=

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  15. If f(x)=(3x-7)/(5x-3) then (fof)(x)=

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  16. If f(x)=-|x|, then (fofof)=

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  17. If f(x)=(x)/(sqrt(1-x^(2))), g(x)=(x)/(sqrt(1+x^(2))) then (fog)(x)=

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  18. If f(x)=log.(1+x)/(1-x) and g(x)=(3x+x^(3))/(1+3x^(2)) then (fog) (x)...

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  19. If f(x)=(x)/(sqrt(1-x^(2))) then (fofof)(x)=

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  20. If f(x)=(x)/(sqrt(1+x^(2))), then (fofof)(x)=

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