Let f:(-1,1)toB be a function defined by...

Let `f:(-1,1)toB` 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

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

B

`[ - po/2, pi/2]`

C

`[0, po/2)`

D

`(0,pi/2)`

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

Let f:RtoR be a function defined by : f(x)=(x^(2)+2x+5)/(x^(2)+x+1) is :

Let f:[2, oo)rarrR be the function defined by f(x)=x^(2)-4x+5 , then the range of f is

The domain of the function defined by f(x)=cos^(-1)sqrt(x-1) is

The domain of the function f defined by : f(x)=(1)/(sqrt(x-|x|)) is :

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.

Let f: R to R be a function defined by : f(x)="Min".{x+1,|x|+1} . Then which of the following is true ?

Let f : R rarr R be a function defined by f(x) = x^3 + 5 . Then f^-1(x) is

The domain of the function f defined by : f(x)=sqrt(4-x)+(1)/(sqrt(x^(2)-1)) is equal to :

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then f is

Show that the function f : R to R , defined by f(x) = 1/x is one-one and onto, where R, is the set of all non-zero real numbers.