Home
Class 12
MATHS
Let f :R to [(3)/(4), oo) be a surjectiv...

Let `f :R to [(3)/(4), oo)` be a surjective quadratic function with line of symmetry `2x -1=0 and f (1) =1`
If `g (x)=(f(x)+f(-x))/(2 ) then int (dx)/(sqrt(g (e ^(x))-2))`is equal to:

A

`sec ^(-1) (e ^(-x))+C`

B

`sec ^(-1) (e ^(x))+C`

C

`sin ^(-1) (e ^(-x)) +C`

D

`sin ^(-1) (e ^(x))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|2 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|29 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|15 Videos

  • HYPERBOLA

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

Let f :R to [(3)/(4), oo) be a surjective quadratic function with line of symmetry 2x -1=0 and f (1) =1 int (e ^(x))/(f (e ^(x)))dx

Let f(x)=2x+1 and g(x)=int(f(x))/(x^(2)(x+1)^(2))dx . If 6g(2)+1=0 then g(-(1)/(2)) is equal to

Let f(x) be a function such that f(x).f(y)=f(x+y) , f(0)=1 , f(1)=4 . If 2g(x)=f(x).(1-g(x))

Let g (x )=f ( x- sqrt( 1-x ^(2))) and f ' (x) =1-x ^(2) then g'(x) equal to:

Let g (x) be then inverse of f (x) such that f '(x) =(1)/(1+ x ^(5)), then (d^(2) (g (x)))/(dx ^(2)) is equal to:

Let g (x) be then inverse of f (x) such that f '(x) =(1)/(1+ x ^(5)), then (d^(2) (g (x)))/(dx ^(2)) is equal to:

Let f (x) be a twice differentiable function defined on (-oo,oo) such that f (x) =f (2-x)and f '((1)/(2 )) =f' ((1)/(4))=0. Then int _(-1) ^(1) f'(1+ x ) x ^(2) e ^(x ^(2))dx is equal to :

Let f : R to R be a continuously differentiable function such that f(2) = 6 and f'(2) = 1/48 . If int_(6)^(f(x)) 4t^(3) dt = (x-2) g(x) than lim_( x to 2) g(x) is equal to

Let f(x) be a continuous function for all x in R and f'(0) =1 then g(x) = f(|x|)-sqrt((1-cos 2x)/(2)), at x=0,

Let g be the inverse function of a differentiable function f and G (x) =(1)/(g (x)). If f (4) =2 and f '(4) =(1)/(16), then the value of (G'(2))^(2) equals to: