Home
Class 12
MATHS
Let f:(-1,1)vecB be a function defined b...

Let `f:(-1,1)vecB` be a function defined by `f(x)=tan^(-1)(2x)/(1-x^2)` . Then `f` is both one-one and onto when `B` is the interval. `[0,pi/2)` (b) `(0,pi/2)` `(-pi/2,pi/2)` (d) `[-pi/2,pi/2]`

A

`(-(pi)/(2), (pi)/(2))`

B

`[-(pi)/(2), (pi)/(2)]`

C

`[0, (pi)/(2))`

D

`(0, (pi)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|10 Videos

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|15 Videos

  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

  • JEE MAIN - 5

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|5 Videos

Similar Questions

Explore conceptually related problems

Let f:(-1,1)rarrB be a function defined by f(x)=tan^(-1)[(2x)/(1-x^2)] . Then f is both one-one and onto when B is the interval. (a) [0,pi/2) (b) (0,pi/2) (c) (-pi/2,pi/2) (d) [-pi/2,pi/2]

Let f:R rarr B , be a function defined f(x)=tan^(-1).(2x)/(sqrt3(1+x^(2))) , then f is both one - one and onto when B, is the interval

One of the root equation cosx-x+1/2=0 lies in the interval (0,pi/2) (b) (-pi/(2,0)) (c) (pi/2,pi) (d) (pi,(3pi)/2)

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)

Range of tan^(-1)((2x)/(1+x^2)) is (a) [-pi/4,pi/4] (b) (-pi/2,pi/2) (c) (-pi/2,pi/4) (d) [pi/4,pi/2]

1.The inverse of cosine function is defined in the intervals (A) [ -pi , 0 ] (B) [ -pi/2,0 ] (C) [ 0,pi/2 ] (D) [ pi/2 , pi ]

One root of the equation cos x-x+1/2=0 lies in the interval (A) [0,pi/2] (B) [-pi/2,0] (C) [pi/2,0] (D) none

Let f : R to [0, pi/2) be defined by f ( x) = tan^(-1) ( 3x^(2) + 6x + a)". If " f(x) is an onto function . then the value of a si

Show that f(x)=tan^(-1)(sinx+cosx) is a decreasing function on the interval on (pi//4,\ pi//2) .

Let f:[pi,3pi//2] to R be a function given by f(x)=[sinx]+[1+sinx]+[2+ sinx] Then , the range of f(x) is