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

Let `f(x)=(sqrt(x-2 sqrt(x-1)))/(sqrt(x-1)-1)`, 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, oo)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Integer Answers Type)|5 Videos
  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Matrix Match Type)|2 Videos
  • DIFFERENTIATION

    CHHAYA PUBLICATION|Exercise EXERCISE 3B (Short Answer Type Questions)|18 Videos
  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a) f^(prime)(10)=1 (b) f^(prime)(3/2)=-1 (c)domain of f(x) is x geq1 (d)range of f(x)i s(-2,-1)uu(2,oo)

If (x+sqrt(x^2-1))/(x-sqrt(x^2-1))+(x-sqrt(x^2-1))/(x+sqrt(x^2-1))= 14 ,then find the value of x.

If f (x) =(1)/(sqrt(x+2sqrt((2x-4))))+(1)/(sqrt(x-2 sqrt(2x-4))) for x gt2, then the value of f (11) is-

int sqrt((1-sqrt(x)))/(1+sqrt(x)).(dx)/(x)

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)

If x = sqrt3/2 then find the value of (sqrt(1+x) - sqrt(1-x))/(sqrt(1+x) + sqrt(1-x))

Solve for x :sqrt(x+1)-sqrt(x-1)=1.

If int(x(x-1))/((x^(2)+1)(x+1)sqrt(x^(3)+x^(2)+x))dx =(1)/(2)log_(e)|(sqrt(f(x))-1)/(sqrt(f(x))+1)|-tan^(-1)sqrt(f(x))+C, then The value of f(1) is

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

Simplify : (x + sqrt(x^(2) - 1))/(x - sqrt(x^(2) -1)) + (x - sqrt(x^(2) -1))/(x + sqrt(x^(2) -1)) If the result of the simplification is equal to 14, then find the value of x