Home
Class 12
MATHS
If the function f:[1,oo)rarr[1,oo) is de...

If the function `f:[1,oo)rarr[1,oo)` is defined by `f(x)=2^(x(x-1)),t h e nf^(-1)(x)` is `(1/2)^(x(x-1))` (b) `1/2(1+sqrt(1+4(log)_2x))` `1/2(1-sqrt(1+(log)_2x)` (d) not defined

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

If the function f:(1,oo)rarr(1,oo) is defined by f(x)=2^(x(x-1)),t h e nf^(-1)(x) is (a) (1/2)^(x(x-1)) (b) 1/2(1+sqrt(1+4(log)_2x)) 1/2(1-sqrt(1+(log)_2x) (d) not defined

If the function f:(1,oo) vec (1,oo) is defined by f(x)=2^(x(x-1)),t h e nf^(-1)(x) is (1/2)^(x(x-1)) (b) 1/2(1+sqrt(1+4(log)_2x)) 1/2(1-sqrt(1+(log)_2x) (d) not defined

If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then f^-1(x) is (A) (1/2)^(x(x-1)) (B) 1/2(1+ sqrt(1+4log_2x) ) (C) 1/2(1-sqrt(1+4log_2x)) (D) not defined

If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then f^-1(x) is (A) (1/2)^(x(x-1)) (B) 1/2 sqrt(1+4log_2x) (C) 1/2(1-sqrt(1+4log_2x)) (D) not defined

If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then f^-1(x) is (A) (1/2)^(x(x-1)) (B) 1/2 sqrt(1+4log_2x) (C) 1/2(1+sqrt(1+4log_2x)) (D) not defined

If f:[1, oo) rarr [1, oo) is defined as f(x) = 3^(x(x-2)) then f^(-1)(x) is equal to

Find the inverse of the function: f:[1, oo) rarr [1,oo),w h e r ef(x)=2^(x(x-2))

The function f:R rarr R defined as f(x)=(x^(2)-x+1)/(x^(2)+x+1) is

If f: Rvec (-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x) equals sqrt((|x|)/(1-|x|)) (b) -sgn(x)sqrt((|x|)/(1-|x|)) -sqrt(x/(1-x)) (d) none of these

If f: Rvec(-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x) equals sqrt((|x|)/(1-|x|)) (b) -sgn(x)sqrt((|x|)/(1-|x|)) -sqrt(x/(1-x)) (d) none of these

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Write the domain of the real function f defined by f(x)=sqrt(25-x^2) .

    Text Solution

    |

  2. Let A}x :-1lt=xlt=1}a n df: Avec A such that f(x)=x|x|, then f is (a) ...

    Text Solution

    |

  3. If the function f:[1,oo)rarr[1,oo) is defined by f(x)=2^(x(x-1)),t h e...

    Text Solution

    |

  4. If f(x)=(x-1)/(x+1),x!=-1, then show that f(f(x))=-1/x provided that x...

    Text Solution

    |

  5. Let f be a real function defined by f(x)=sqrt(x-1.) Find (fofof)(x)dot...

    Text Solution

    |

  6. Let f: R-> R be the function defined by f(x)=4x−3 for all x in R. Then...

    Text Solution

    |

  7. Find whether f: R->R given by f(x)=x^3+2 for all x in R .

    Text Solution

    |

  8. Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

    Text Solution

    |

  9. Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , i...

    Text Solution

    |

  10. Discuss the surjectivity of f: R->R given by f(x)=x^3+2 for all x i...

    Text Solution

    |

  11. Discuss the surjectivity of f: R->R given by f(x)=x^2+2 for all x i...

    Text Solution

    |

  12. Discuss the surjectivity of f: Z->Z given by f(x)=3x+2 for all x in...

    Text Solution

    |

  13. Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for e...

    Text Solution

    |

  14. Show that the Signum function f:R->R, given by f(x)={(1,xgt0),(0,x=0),...

    Text Solution

    |

  15. Prove that the function f: Q->Q given by f(x)=2x-3 for all x in Q ...

    Text Solution

    |

  16. Show that the function f: R->R defined by f(x)=3x^3+5 for all x in R ...

    Text Solution

    |

  17. Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(...

    Text Solution

    |

  18. Let A be the set of all 50 students of class X I I in a central scho...

    Text Solution

    |

  19. Show that the function f: N->N , given by f(x)=2x , is one-one but not...

    Text Solution

    |

  20. Prove that f: R->R , given by f(x)=2x , is one-one and onto.

    Text Solution

    |