Home
Class 12
MATHS
Two functions f:Rrarr R, g:R rarr R are ...

Two functions `f:Rrarr R, g:R rarr R` are defined as follows :
`f(x)={{:(0,"(x rational)"),(1,"(x irrational)"):}," " g(x)={{:(-1,"(x rational)"),(0,"(x irrational)"):}` then `(fog)(pi)+(gof)(e)=`

A

`-1`

B

0

C

1

D

2

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B(DOMAINS, RANGES OF REAL FUNCTIONS)|138 Videos

  • FUNCTIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS)|7 Videos

  • FUNCTIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS)|7 Videos

  • EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 4|5 Videos

  • Hyperbola

    DIPTI PUBLICATION ( AP EAMET)|Exercise SET 4|4 Videos

Similar Questions

Explore conceptually related problems

If the functions f(x) and g(x) are defined on R rarr R such that f(x) ={:{(0, x in " rational "),( x, x in " irrational ") :} g(x) ={:{(0, x in " irrational ") ,(x, x in " rational "):} then (f-g) (x) is

If f:R rarr R, g:R rarr R are defined by f(x)=x^(2)+2x-3, g(x)=3x-4 , then (fog)(-1)=

If f:R rarr R, S: R rarr R are defined by f(x) = 3x-4, g(x) = 5x-1 then, (fog^(-1))(2) =

If f:R rarr R, g:R rarr R are defined by f(x)=4x-1, g(x)=x^(3)+2, then (gof)((a+1)/(4))=

If f:R rarr R, g:R rarr R are defined by f(x)= 5x-3,g(x)=x^(2)+3 , then (gof^(-1))(3)=

If f,g:R to R are defined f(x) = {(0 if , x in Q),(1 if, x in Q):}, g(x) = {(-1 if , x in Q),(0 if, x !in Q):} then find (fog)(pi)+(gof)(e ) .

If f:R rarrR, g:R rarrR are defined by f(x)=3x-2, g(x)=x^(2)+1 , then (fog)(x^(2)+1)=

DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
  1. If f(x)=x^(2), g(x)=x^(2)-5x+6 then (g(2)+g(2)+g(0))/(f(0)+f(1)+f(-2))...

    Text Solution

    |

  2. f(x)=1, if x rational, =0, if x is irrational. Then (f(1//2)+f(sqrt5...

    Text Solution

    |

  3. Two functions f:Rrarr R, g:R rarr R are defined as follows : f(x)={{...

    Text Solution

    |

  4. If f:Rrarr R is defined by f(x)=3x-2, then (f(o)f) (x)+2=

    Text Solution

    |

  5. If f(x)=sqrt(x^(3)-1) and g(x)=root(3)(x^(2)+1), then (fog)(x)=

    Text Solution

    |

  6. f:R rarr R, defined by f(x)=sinx and g:R rarrR, defined by g(x)=x^(2),...

    Text Solution

    |

  7. If f:R rarr R, g:R rarr R are defined by f(x)=x^(2)+2x-3, g(x)=3x-4, t...

    Text Solution

    |

  8. If f:R rarr R, g:R rarr R are defined by f(x)=4x-1, g(x)=x^(3)+2, then...

    Text Solution

    |

  9. If f:R rarrR, g:R rarrR are defined by f(x)=3x-2, g(x)=x^(2)+1, then (...

    Text Solution

    |

  10. Let g(x)=1+x-[x] and f(x)=-1 if x lt 0 =0 if x=0 then f[g(x)]= =1 ...

    Text Solution

    |

  11. If f(x)={{:(x^(3)+1",",x lt0),(x^(2)+1",", x ge0):}, g(x)={{:((x-1)^(1...

    Text Solution

    |

  12. If f(x)=x^(3)-x, g(x)=sin 2x, then

    Text Solution

    |

  13. If f(x)=logx, g(x)=x^(3) then f[g(a)]+f[g(b)]=

    Text Solution

    |

  14. If f:R rarrR and g:R rarrR are defined by f(x)=2x+3, g(x)=x^(2)+7 then...

    Text Solution

    |

  15. If f:RR rarrRR and g:RR rarrRR are defined by f(x)=2x+3 and g(x)=x^(2)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |