Home
Class 12
MATHS
If f: Rvec (-1,1) is defined by f(x)=-...

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

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 f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is invertible, find f^(-1)

If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is invertible, find f^(-1)

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)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

If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals. (x+sqrt(x^2-4))/2 (b) x/(1+x^2) (c) (x-sqrt(x^2-4))/2 (d) 1+sqrt(x^2-4)

If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals. (x+sqrt(x^2-4))/2 (b) x/(1+x^2) (c) (x-sqrt(x^2-4))/2 1+sqrt(x^2-4)

If f(x) =(x-4)/(2sqrt(x)) , then f^(')(1) is equal to

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)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

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Show that f: R-[0]->R-[0] given by f(x)=3/x is invertible and it is in...

    Text Solution

    |

  2. Let A={1,2,..., n} and B={a , b }. Then number of surjections from A...

    Text Solution

    |

  3. If f: Rvec (-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x...

    Text Solution

    |

  4. Let f: ZrarrZ be defined by f(n)=3n for all n in Z and g: ZrarrZ be d...

    Text Solution

    |

  5. Let A={x in R :0lt=xlt=1}dot If f: A->A is defined by f(x)={(x ,, if ...

    Text Solution

    |

  6. Let A=[-1,1]dot Then, discuss whether the following functions from A t...

    Text Solution

    |

  7. Let R be a relation on the set A of ordered pairs of positive intege...

    Text Solution

    |

  8. Let A be a finite set. If f: AvecA is an onto function, show that f is...

    Text Solution

    |

  9. Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is ...

    Text Solution

    |

  10. Show that the function f: Rvec R given by f(x)=x^3+x is a bijection.

    Text Solution

    |

  11. Let f: Nuu{0}->Nuu{0} be defined by f={(n+1 ,, ifn \ i s \ e v e n),(n...

    Text Solution

    |

  12. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

    Text Solution

    |

  13. Let A={1,2} . Find all one-to-one function from A to A.

    Text Solution

    |

  14. Let f: Rveca n dg: RvecR be defined by f(x)=x+1a n dg(x)=x-1. Show tha...

    Text Solution

    |

  15. Verify assoiativity for the following three mappings : f: N->Z0 (t...

    Text Solution

    |

  16. If the set A contains 5 elements and the set B contains 6 elements, th...

    Text Solution

    |

  17. If the set A contains 7 elements and the set B contains 10 elements, ...

    Text Solution

    |

  18. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

    Text Solution

    |

  19. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  20. Let A={1,2,3}dot Write all one-one from A to itself.

    Text Solution

    |