IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

raju111

find the inverse of x+sinx if x (o,pi).

akhil_o

can tell u th grph of the inverse..if not the invrse.

graph of x+sin x is shown below.

Graph of inerse can b obtained by taking reflection about line y=x

akhil_o

It looks like the graph of x-sinx.

BUT IT IS NOT THE INVERSE

man111

can u tell me what is the expression for f^-1(x)

is expression is x-sinx.

man111

so what will be the expression for f^-1(x)

suppose that i want to integrate f^-1(x)

so how we can done this thing.

man111

akhil can u tell me

what will be the expression for f^-1(x).

bcz i want ti intigrate f^-1(x)..

akhil_o

Integrate x-sinx from 0-pi,

i think it shd work by graph

so we get x²/2+cos x=

²/2-1-1=

²/2-2

Just tell me if its the right answer

but i'm pretty sure no inverse is really clearly defined

rate if helpful and plz post the correct answer

yogesh13

inverse of given function dosent exist

johri_anshuman

here is the exact graph made using software

the inverse of x + sin(x) exists and can be found using graph...

f^--1(x) is not x - sin(x) coz x - sin(x) is not the exact mirror image of x+sin(x) on y=x

blue -> x+sinx
red -> x- sinx

yogesh13

to exist inverse d function should b bijective.but it is not bijective bcoz the derivative of function should b monotonic but it is not monotonic

biki

hey .... yogesh...

the inverse of the function exists...

f ' (x) = 1 + cos(x)

now in (0,pi) sign of cos(x) changes as + from (0,pi/2) and - from (pi/2,pi)

and = 0 when x = pi/2

but keeping in mind that value of Icos(x)I

1 it can b said that f ' (x) is positive in (0,pi) as in (0,pi/2) cos(x) is positive and also in (pi/2,pi) cos(x) is negative but Icos(x)I

1 na ....

So f ' (x) > 0 in (0,pi) na ???

so f ^-1(x) exists.... i guess

biki

hey anshuman .... we share same names buddy

ok can u tell me what software is that??? ... cool one man

johri_anshuman

u can dwld that software from www.padowan.dk

it updates itself when a newer version is available...

biki

what abt da answer 2 dat ques. ??

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