Home
Class 11
MATHS
If f(x) = sin x + cos x , g(x) =x^2 - 1 ...

If f(x) = sin x + cos x , g(x) =`x^2 - 1` then show that g(f(x)) is invertible in the domain `[-pi/4 , pi/4]`.

Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    PATHFINDER|Exercise QUESTION BANK|296 Videos

  • LIMIT, CONTINUITY AND DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|293 Videos

Similar Questions

Explore conceptually related problems

If f(x)=sinx+cosx and g(x)=x^2-1 , then g(f (x)) is invertible in the domain ?.

Let f(x)=sin x+cosx and g(x)=x^(2)-1 , then g{f(x)} is invertible if -

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

If f(x)={x^2 sin((pi x)/2), |x| =1 then f(x) is

If f(x) = (1−x)^(1/2) and g(x)=ln(x) then the domain of (gof)(x) is

If g(x)=int_(0)^(x)cos^(4)t dt , then prove that g(x+pi)=g(x)+g(pi) .

If f(x) = cos[pi^2]x + cos[-pi^2]x , where [x] stands for the greatest integer function, then find f(pi/2),f(pi/4) .

If f(x)=sin3x cos4x , then the value of f''((pi)/(2)) is -

Show that, the function f(x)=cos 2x is increasing at x=(3pi)/4 .

Let f(x)=sin^(23)x-cos^(22)xa n dg(x)=1+1/2tan^(-1)|x| . Then the number of values of x in the interval [-10pi,8pi] satisfying the equation f(x)=sgn(g(x)) is __________

PATHFINDER-FUNCTIONS-QUESTION BANK
  1. f is a function such that f(x + y) = f(x) .f(y),forall x, y in R , if ...

    Text Solution

    |

  2. Find domain of f(x) = sqrt(1 - sqrt(1-sqrt(1 - x^2))).

    Text Solution

    |

  3. If f(x) = sin x + cos x , g(x) =x^2 - 1 then show that g(f(x)) is inve...

    Text Solution

    |

  4. If f(x) = 4^x/(4^x + 2), then find f(x) + f(1 - x).

    Text Solution

    |

  5. If 2f(x) - 3f(1/x) =x^2 (x ne 0), then find f(2).

    Text Solution

    |

  6. If f(x) =cos[pi^2]x + cos[-pi^2]x, where [x] stands for the greatest i...

    Text Solution

    |

  7. Find the range of f(x)=(x^2 + x +2)/(x^2 + x +1) (-infty lt x lt infty...

    Text Solution

    |

  8. Find the domain of definition of the function f(x) = 1/sqrt(absx + x).

    Text Solution

    |

  9. If f : RrarrR such that f(x) = x - [x], where [p] denotes the greatest...

    Text Solution

    |

  10. Find the range of the function f(x) = x^2 + 1/(x^2 + 1).

    Text Solution

    |

  11. Find the range of the function phi where phi(x) = cos^-1 (x^2/(1 + x^2...

    Text Solution

    |

  12. Find the range of the function f(x) =abs(x - 1) + abs(x - 2) , -1 le x...

    Text Solution

    |

  13. Find the range of the function y = log3 (5 + 4x - x^2).

    Text Solution

    |

  14. If f(x + y) = f(x) - f(y),forall x, y in R, then show that f(3) = f(1)

    Text Solution

    |

  15. Find the range of the function f(x) = (e^x - e^-x).

    Text Solution

    |

  16. Find the inverse function of the function f(x) = [4 - (x - 7)^3]^(1/5)...

    Text Solution

    |

  17. If f(x) =e^(x + a) , g(x) = x^(b^2) and h(x) = e^(b^2 x), then find th...

    Text Solution

    |

  18. Find domain of the function f(x) = 2^sin^(-1)x + 1/sqrt(x - 2).

    Text Solution

    |

  19. Prove that the domain of g(x) =cot^-1 x/sqrt(x^2 - [x]) , x in R is R ...

    Text Solution

    |

  20. Find the range of the function y =1/(2 - cos 2x).

    Text Solution

    |