Home
Class 12
MATHS
If F :[1,oo)->[2,oo) is given by f(x)=x+...

If `F :[1,oo)->[2,oo)` is given by `f(x)=x+1/x ,t h e n \ f^(-1)(x)` equals ` \ \ ` (a)`(x+sqrt(x^2-4))/2` (b) `x/(1+x^2)` (c) `(x-sqrt(x^2-4))/2` (d)`1+sqrt(x^2-4)`

A

`(x+sqrt(x^(2)-4))/2`

B

`x/(1+x^(2))`

C

`(x-sqrt(x^(2)-4))/2`

D

`1+sqrt(x^(2)-4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise FUNCTION EXERCISE 8:Questions Asked in Previous 10 Years Exams|1 Videos

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise FUNCTION EXERCISE 7: Subjective Type Questions|1 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

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:[1,oo)->[2,oo) is given by f(x)=x+1/x then f^-1(x) equals to : a) (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(x)=sqrt(1-sin2x), then f'(x) equals

If f(x)=sin^2x and the composite function g(f(x))=|sinx| , then g(x) is equal to (a) sqrt(x-1) (b) sqrt(x) (c) sqrt(x+1) (d) -sqrt(x)

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

If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

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: 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 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

ARIHANT MATHS ENGLISH-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The function f:[0,3]vec[1, 29], defined by f(x)=2x^3-15 x^2+36 x+1, is...

    Text Solution

    |

  2. Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x sat...

    Text Solution

    |

  3. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  6. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

    Text Solution

    |

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

    Text Solution

    |

  8. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  9. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo)...

    Text Solution

    |

  10. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  11. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  12. Let E={1,2,3,4}a n dF-{1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  13. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  14. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  15. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

    Text Solution

    |

  16. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

    Text Solution

    |

  17. Let f(x)=(alphax)/((x+1)),x!=-1. The for what value of alpha is f(f(x)...

    Text Solution

    |

  18. Let g(x)=1+x-[x] and f(x)={-1,x < 0 0, x=0 1, x > 0. Then for all...

    Text Solution

    |

  19. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |

  20. Let f(theta)=sintheta(sintheta+sin3theta)dot Then f(theta)i s geq0on ...

    Text Solution

    |