Home
Class 12
MATHS
If g(f(x))=|sin x| and f(g(x))=(sin sqrt...

If `g(f(x))=|sin x|` and `f(g(x))=(sin sqrt(x))^(2)` then

A

`f(x)=sin ^(2) x, g(x)=sqrt(x)`

B

`f(x)=sin x, g(x)=|x|`

C

`f(x)=x^(2), g(x)=sin sqrt(x)`

D

f and g cannot be determined

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS AND EXPRESSION

    HIMALAYA PUBLICATION|Exercise Question Bank|129 Videos

  • STATISTICS MEASURE OF DIPERSION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|28 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = |sin x|. Then

If g(x) = 1+sqrtx and f(g(x))=3+2sqrtx+x then f(x) =

If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x and g(x) = x^(2) , then find the values of (fog) (sqrt(pi))/(2) "and (gof)"((pi)/(3)) .

If y = f((2x-1)/(x^(2)+1)) and f^(')(x) = sin x^(2) , then dy/dx =

If f:R -> R, g:R -> R defined as f(x) = sin x and g(x) = x^2 , then find the value of (gof)(x) and (fog)(x) and also prove that gof != fog .

If f(x) = ax+b and g(x) = cx+d then f(g(x)) = g(f(x)) is equivalent to

HIMALAYA PUBLICATION-SETS,RELATIONS AND FUNCTIONS-QUESTION BANK
  1. If f: (R) rarr (R) and g (R) rarr (R) defined by f(x)=2x+3andg(x)=x^(2...

    Text Solution

    |

  2. Let g(x)=1+x-[x] and f(x)={:{(-1","x<0),(0","x=0),(1","x>0):} Then fo...

    Text Solution

    |

  3. If g(f(x))=|sin x| and f(g(x))=(sin sqrt(x))^(2) then

    Text Solution

    |

  4. Prove that cos ^(2) x + cos ^(2) (x + (pi)/(3) + cos ^(2) (x - (pi)/(...

    Text Solution

    |

  5. If e^(f(x))=(10+x)/(10-x), x in(-10,10) and f(x)=k f((200 x)/(100+x^(...

    Text Solution

    |

  6. Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)), x ne 0, then f(x)=

    Text Solution

    |

  7. If f(x)=(1)/(sqrt(x+2 sqrt(2 x-4)))+(1)/(sqrt(x-2 sqrt(2 x-4))), for x...

    Text Solution

    |

  8. Let X={1,2,3,4}, then one-one onto mappings f:XtoX such that f(1)=1,f(...

    Text Solution

    |

  9. Let, f: R rarr R be given by f(x)=(x+1)^(2)-1, x ge-1 . Then the set...

    Text Solution

    |

  10. Let f: R rarr R be given by f(x)=(x+1)^(2)-1, x ge-1 . Then f^(-1)(x)...

    Text Solution

    |

  11. Suppose f(x)=(x+1)^(2) for xge-1. If g(x) is the function whose graph ...

    Text Solution

    |

  12. Let f : R rarr R be defined by f(x)=2 x+|x| then f(2 x)+f(-x)-f(x)=

    Text Solution

    |

  13. If f:[1,oo)to[1,oo) is given by f(x)=x+(1)/(x), then f^(-1)(x) equals ...

    Text Solution

    |

  14. If f:[1,oo)to[2,oo) is given by f(x)=x+(1)/(x), then f^(-1)(x) equals ...

    Text Solution

    |

  15. Let f(theta) =sin theta(sin theta + sin3theta) then f(theta) :

    Text Solution

    |

  16. If f(x)=3 x-5, then f^(-1)(x)=

    Text Solution

    |

  17. If f(1)=1 and f(n+1)=2 f(n)+1, then f(n) is

    Text Solution

    |

  18. If f(x)=alpha x^(2)+b x+c, then the values of a and b for which the i...

    Text Solution

    |

  19. If f(x)=1+alphax,alphane0 is the inverse of itself, then the value of ...

    Text Solution

    |

  20. Let f:[0.1] rarr[0,1] and g:[0,1] rarr[0,1] be two functions defined b...

    Text Solution

    |