Differential Calculus

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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



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shiva  kumar's Avatar

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9 Dec 2009 21:09:10 IST
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is ans x-sinx
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9 Dec 2009 22:00:04 IST
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EXPLAIN 

shiva  kumar's Avatar

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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
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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
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9 Dec 2009 23:37:44 IST
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since this function is not bijective so the inverse does not exists...........
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9 Dec 2009 23:38:44 IST
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since this function is not bijective so the inverse does not exists...........

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10 Dec 2009 00:22:04 IST
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The function is both one-one as well as onto since  
for all real x.i.e.f(x)  is an increasing function and will never repeat its value
From the graph it appears as if the inverse isf^{-1}(x)=x-sinx  since it appears to be reflection of f(x)   with respect to the line  y=x as mirror.

I am not sure about this though

The wicked warrior ''Anurag the devil'''s Avatar

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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]
The wicked warrior ''Anurag the devil'''s Avatar

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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....
shiva  kumar's Avatar

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10 Dec 2009 14:06:13 IST
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MAN THIS FN IS BIJECTIVE FOR ALL X
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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)...

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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.

 

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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
The wicked warrior ''Anurag the devil'''s Avatar

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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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