|

Algebra

Scorching goIITian

 Joined: 31 Oct 2007 Post: 227
1 Feb 2008 19:07:22 IST
0 People liked this
27
1496
brain twister
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

f(x)=x(4-x) find f inverse

• 1
• 2
• GO
• Go to Page...

Blazing goIITian

Joined: 17 Jan 2008
Posts: 1451
1 Feb 2008 19:13:51 IST
0 people liked this

i am gettin the inverse as
2+-2-x

first take y=4x-x2
now do it by quadratic roots method

rate if right
nudge if wrong

Blazing goIITian

Joined: 9 Jan 2008
Posts: 843
1 Feb 2008 19:17:33 IST
0 people liked this

same  here!!

Scorching goIITian

Joined: 31 Oct 2007
Posts: 227
1 Feb 2008 19:20:27 IST
1 people liked this

see my solution.
f(f1(x))=4f(1x)-f(1x)^2
lhs=x
solving this we get
f(1x)=2+r00t3,2-root3
rate me if useful

Blazing goIITian

Joined: 17 Jan 2008
Posts: 1451
1 Feb 2008 19:22:25 IST
0 people liked this

rockey ...how come u get a linear answer?
it shd be dependent on x atleast!
hav a look at what i've done

Blazing goIITian

Joined: 6 May 2007
Posts: 1041
1 Feb 2008 19:23:10 IST
0 people liked this

Inverse of a function exists only when the function is bijective

Quadratic expressions are not bijective , hence inverse dosent exist...

Scorching goIITian

Joined: 31 Oct 2007
Posts: 227
1 Feb 2008 19:29:27 IST
1 people liked this

sorry.
the ans is 2+root of(4-x),2-rootof (4-x)

Blazing goIITian

Joined: 9 Jan 2008
Posts: 843
1 Feb 2008 19:32:34 IST
0 people liked this

Check whether it is one-one  and onto

for onto
if  f(x)  belongs to RR  then  f(x) is not onto
let y=x(4-x)

u get

x=2+-root(4-y)

As 4-y>=0
thus  y<=4

u see that ranges are diff. when compared with f(x)

Scorching goIITian

Joined: 31 Oct 2007
Posts: 227
1 Feb 2008 19:32:35 IST
0 people liked this

srujana u r wrong. some QE are bijectives.

Scorching goIITian

Joined: 31 Oct 2007
Posts: 227
1 Feb 2008 19:38:58 IST
0 people liked this

raul you should also get x=2-root(4-y)
by my method you can get both roots

New kid on the Block

Joined: 26 Dec 2007
Posts: 15
1 Feb 2008 19:41:09 IST
0 people liked this

hi i think the answer is 2+sq.root(4+x) or 2-sq.root(4+x)
if correct check tis out
taking 4x-x.x=y
find x in terms of y

Scorching goIITian

Joined: 31 Oct 2007
Posts: 227
1 Feb 2008 19:43:11 IST
0 people liked this

i have given the solution & ans above check it.

New kid on the Block

Joined: 26 Dec 2007
Posts: 15
1 Feb 2008 19:44:34 IST
0 people liked this

New kid on the Block

Joined: 26 Dec 2007
Posts: 15
1 Feb 2008 19:45:57 IST
0 people liked this

is my explanations clear

Blazing goIITian

Joined: 31 Jan 2008
Posts: 334
1 Feb 2008 19:58:45 IST
2 people liked this

look i am sending u a trick
plz. rate me for it......
when u want to get some inverse, then just exchange the places of x and y. u can know it if u apply pure logic. remember: (f inv.) is reflection of f on line y=x
like here-
x= y(4-y)
if u like this method then plz. rate

Blazing goIITian

Joined: 22 Jan 2007
Posts: 2039
1 Feb 2008 21:49:48 IST
0 people liked this

i agree with saurabh...

Moderator
Joined: 16 Dec 2006
Posts: 3373
1 Feb 2008 22:25:19 IST
0 people liked this

y = x(4-x)
y = 4x - x^2
y - 4x + x^2 = 0
x^2 - 4x + y = 0
x = 4 +- sqrt (16 - 4y) / 2
x = 4 +- 2 rt (4 - y) / 2
x = 2 +- sqrt (4-y)

so inverse is :
y = 2 +- sqrt (4-x)

Cool goIITian

Joined: 29 Sep 2007
Posts: 65
1 Feb 2008 22:29:01 IST
0 people liked this

x2 - 4x +y = 0

x = 2 (4-y)1/2

f-1 (y) = 2 + (4-y)1/2 , 2 - (4-y)1/2

f-1 (x) = 2 + (4-x)1/2 , 2 - (4-x)1/2

Cool goIITian

Joined: 18 Jan 2008
Posts: 41
1 Feb 2008 22:51:59 IST
0 people liked this

saurabh can we apply ur method in every case to find inverse of a function??????

Moderator
Joined: 16 Dec 2006
Posts: 3373
1 Feb 2008 22:57:53 IST
0 people liked this

ohho mr. saurabh!

u exchange the places of x and y only after uve written the equation in terms of x = something..
and not straightaway,,, ur committing a grave error!

 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