Home
Class 12
MATHS
Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)...

Let `f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1).x` then

A

`f(10)=1`

B

`f'(3//2)=-1`

C

domain of `f(x) is x ge 1`

D

range of `f(x) is (-2, -1)] cup (2,00)`

Text Solution

Verified by Experts

`f(x)(sqrt((x-1)^(2))+1-2sqrt(x-1))/(sqrt(x-1)-1)`
`=(|sqrt(x-1)-1|)/(sqrt(x-1)-1)x`
`={{:(-x",", if x in [1,2)),(x",", if x in (2,oo)):}`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|24 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Matrix Match Type|6 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Execrises|137 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

The expression (1)/(sqrt(x+2sqrt(x-1)))+(1)/(sqrt(x-2sqrt(x-1))) simplifies to:

Differentiate w.r.t 'x' f(x) = (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1))

If f:RtoR,f(x)=(sqrt(x^(2)+1)-3x)/(sqrt(x^(2)+1)+x) then find the range of f(x) .

If f(x) = sqrt(x+2sqrt(x+1)) + sqrt(x-2sqrt(x-1)), x ge 1 . Statement-1 : Then, f(x) = 2 , when x in [1, 2] and Statement-2 : sqrt((f(x))^(2)) = {{:(f(x)",", f(x) ge 0),(-f(x)",", f(x) lt 0):}

let f(x)=sqrt(1+x^2) then

If f(x)=(1)/(sqrt(x+2sqrt(2x-4)))+(1)/(sqrt(x-2sqrt(2x-4))) for xgt2 then find f(11).

Find the value of sqrt((x+2sqrt((x-1)))]+sqrt((x-2sqrt((x-1)))] =

Consider the function f(x)=(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cos x)) then Q. If x in (pi, 2pi) then f(x) is

Let f(x)=tan^(-1)((sqrt(1+x^(2))-1)/(x)) then which of the following is correct :

Let f(x)=tan^(-1)((sqrt(1+x^(2))-1)/(x)) then which of the following is correct :

CENGAGE ENGLISH-DIFFERENTIATION-Multiple Correct Answers Type
  1. "If "f(theta)=tan (sin^(-1)sqrt((2)/(3+cos 2theta)))," then " fi nd f'...

    Text Solution

    |

  2. f(x)=|x^(2)-3x|x|+2|. Then which of the following is/are true ?

    Text Solution

    |

  3. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1).x then

    Text Solution

    |

  4. If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n y^(prime)(1)=4/3 (b) y^(1)...

    Text Solution

    |

  5. If y=x^((logx)^log(logx)) then (dy)/(dx)=

    Text Solution

    |

  6. If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne...

    Text Solution

    |

  7. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (-2)/(1+x^2) for all ...

    Text Solution

    |

  8. f(n)(x)=e^(f(n-1)(x))" for all "n in N and f(0)(x)=x," then "(d)/(dx){...

    Text Solution

    |

  9. Suppose f and g are functions having second derivatives f' and g' ever...

    Text Solution

    |

  10. If y=e^(-x) cos x and yn+kny=0 where yn=(d^ny)/(dx^n) and kn are const...

    Text Solution

    |

  11. If a function is represented parametrically be the equations x=(1+(lo...

    Text Solution

    |

  12. If y=(x^2)/2+1/2xsqrt(x^2+1)+1/2(log)esqrt(x+sqrt(x^2+1)) , prove that...

    Text Solution

    |

  13. A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in ...

    Text Solution

    |

  14. "If "e^(sin(x^(2)+y^(2)))=tan""(y^(2))/(4)+sin^(-1)x," then y'(0) can ...

    Text Solution

    |

  15. If g is the inverse of a function f and f^'(x)=1/(1+x^5) then g^'(x) i...

    Text Solution

    |

  16. If for x (0,1/4), the derivative of tan^(-1)((6xsqrt(x))/(1-9x^3)) is ...

    Text Solution

    |

  17. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

    Text Solution

    |

  18. Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x ...

    Text Solution

    |

  19. Let f:R to R and h:R to R be differentiable functions such that f(x)=x...

    Text Solution

    |

  20. If y=e^(sqrt(x))+e^(-sqrt(x))," then "(dy)/(dx) is equal to

    Text Solution

    |