|

Differential Calculus

New kid on the Block

 Joined: 8 May 2012 Post: 14
15 Jun 2012 17:03:52 IST
0 People liked this
1
292
Domain And Range
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Differential Calculus

Consider the real valued function satisfying      2f (sin x) + f (cos x) = x  .   Find domain And Range of f(x).

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
16 Jun 2012 14:15:39 IST
0 people liked this

see we can give any value to x here so the domain would be r

put x=sin^-1x

2f(x)+f((1-x^2)^1/2)=sin^-1x

put x=cos^-1x

2f((1-x^2)^0.5)+f(x)=cos^-1x

solve these equation

F(x)=(2sin-1x-cos^-1x)/3

F(x)=(pi-3*cos^-1x)/3

range would be(-2*pi/3,pi/3)

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

### Find Posts by Topics

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 9960 m Post - 2185
4. edison
 Altitude - 10815 m Post - 7797
5. Sagar Saxena
 Altitude - 8625 m Post - 8064