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Differential Calculus

Blazing goIITian

 Joined: 23 Jun 2009 Post: 448
9 Dec 2009 20:49:29 IST
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inverse function of the function f(x)=x+sinx
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Differential Calculus

inverse function of the function f(x)=x+sinx

Cool goIITian

Joined: 5 Dec 2009
Posts: 54
9 Dec 2009 21:09:10 IST
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is ans x-sinx

Blazing goIITian

Joined: 23 Jun 2009
Posts: 448
9 Dec 2009 22:00:04 IST
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EXPLAIN

Cool goIITian

Joined: 5 Dec 2009
Posts: 54
9 Dec 2009 22:59:34 IST
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OBSERVE X+SINX GRAPH IT IS SINX (IN CURVATURE ) B/W X+1 AND X-1.X-SINX COMES OUT TO BE INVERSE GRAPH SHIFT X+SINX IN Y=X GRAPH

Cool goIITian

Joined: 5 Dec 2009
Posts: 54
9 Dec 2009 22:59:41 IST
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OBSERVE X+SINX GRAPH IT IS SINX (IN CURVATURE ) B/W X+1 AND X-1.X-SINX COMES OUT TO BE INVERSE GRAPH SHIFT X+SINX IN Y=X GRAPH

Blazing goIITian

Joined: 28 Oct 2009
Posts: 594
9 Dec 2009 23:37:44 IST
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since this function is not bijective so the inverse does not exists...........

Blazing goIITian

Joined: 28 Oct 2009
Posts: 594
9 Dec 2009 23:38:44 IST
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since this function is not bijective so the inverse does not exists...........

Blazing goIITian

Joined: 23 Sep 2007
Posts: 966
10 Dec 2009 00:22:04 IST
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The function is both one-one as well as onto since $f^{'}(x)= 1+cos x\geq 0$
for all real x.i.e.  is an increasing function and will never repeat its value
From the graph it appears as if the inverse is  since it appears to be reflection of    with respect to the line   as mirror.

Blazing goIITian

Joined: 28 Oct 2009
Posts: 594
10 Dec 2009 13:48:43 IST
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hey this function is bijective only for x belongs to[-pi/2,pi/2]

Blazing goIITian

Joined: 28 Oct 2009
Posts: 594
10 Dec 2009 13:49:23 IST
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in the questio nothing is mentioned about the value of x so this function is not invertible....

Cool goIITian

Joined: 5 Dec 2009
Posts: 54
10 Dec 2009 14:06:13 IST
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MAN THIS FN IS BIJECTIVE FOR ALL X

Blazing goIITian

Joined: 5 Sep 2008
Posts: 953
10 Dec 2009 20:49:14 IST
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The function is a Bijection, as for every "x" there is one n only one value of "y"....

And its inverse is rightly (x-sinx)...

Forum Expert
Joined: 23 Oct 2009
Posts: 580
10 Dec 2009 21:36:09 IST
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if ƒ is the function

$f(x) = x + sin x , ,!$

then ƒ is one-to-one, and therefore possesses an inverse function ƒ−1. There is no simple formula for this inverse, since the equation y = x + sin x cannot be solved algebraically for x.

But answer is x-sinx as it was well  explained by above people.

Blazing goIITian

Joined: 28 Oct 2009
Posts: 594
11 Dec 2009 09:41:13 IST
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hey but i think its bijective only for x belongs to [-pi/2,pi/2]...........if in question this is mention then i agree with jesh and others

Blazing goIITian

Joined: 28 Oct 2009
Posts: 594
11 Dec 2009 10:11:42 IST
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oh sorry i got it theres no way for common value becoz its x+ sinx and may be sinx oscillates but the total value will not osccilate .....ok thanx to all of u

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