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1 Feb 2008 19:07:22 IST

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Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

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

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Akhil

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1 Feb 2008 19:13:51 IST

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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

Rahul Raghavendra

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1 Feb 2008 19:17:33 IST

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same here!!

rockey

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1 Feb 2008 19:20:27 IST

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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

Akhil

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1 Feb 2008 19:22:25 IST

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

Srujana

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1 Feb 2008 19:23:10 IST

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Inverse of a function exists only when the function is bijective

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

rockey

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1 Feb 2008 19:29:27 IST

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

Rahul Raghavendra

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1 Feb 2008 19:32:34 IST

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Check whether it is one-one and onto

for onto

if f(x) belongs to R

R then f(x) is not onto

let y=x(4-x)

solve quadriatic

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)

rockey

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1 Feb 2008 19:32:35 IST

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srujana u r wrong. some QE are bijectives.

rockey

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1 Feb 2008 19:38:58 IST

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

krishna harsha

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1 Feb 2008 19:41:09 IST

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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

rockey

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1 Feb 2008 19:43:11 IST

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i have given the solution & ans above check it.

krishna harsha

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1 Feb 2008 19:44:34 IST

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rate the reply: [?]

krishna harsha

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1 Feb 2008 19:45:57 IST

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is my explanations clear

saurabh panda

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1 Feb 2008 19:58:45 IST

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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

Neeraj Agarwal

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1 Feb 2008 21:49:48 IST

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i agree with saurabh...

Gaurav |spideyunlimited| Ragtah

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1 Feb 2008 22:25:19 IST

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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)

Nikhil Krishna

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1 Feb 2008 22:29:01 IST

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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

nikita chowdhary

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1 Feb 2008 22:51:59 IST

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

Gaurav |spideyunlimited| Ragtah

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1 Feb 2008 22:57:53 IST

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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!

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