Taking Image of a curve about a given line

In summary, finding the image of a function about a given line involves reflecting the function around the line. This can also be done with functions, but they may not always be explicitly solvable. The functions $f(x)= x + sinx$ and $f(x)= y + sin y$ are symmetric around $y=x$ and intersect at the point $(2\pi,2\pi)$. The area under $g$ between the limits is $2\pi^2$, resulting in an answer of $2$.
  • #1
DaalChawal
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How to find image of $f(x)= x + sinx$ about the given line $y = - x$ .

Similarly can we take image of a function about a function? OR is it necessary about which we take image should be a point, line only?
 
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  • #2
If $y=x+\sin x$, then the reflection around $y=-x$ is $-x=-y+\sin(-y)$ or $x=y+\sin y$. Although a function, this cannot be explicitly solved for $y$. However the two functions are also symmetric around $y=x$ and intersect at the point $(2\pi,2\pi)$. So the area under $g$ between your limits is $2\pi^2$ so your answer is $2$.
 

FAQ: Taking Image of a curve about a given line

How do you take an image of a curve about a given line?

To take an image of a curve about a given line, you first need to have a clear understanding of the curve and the line. Then, you can use a mathematical equation or software program to plot the curve and line on a graph. Finally, you can take a screenshot or print the graph to capture the image.

What is the purpose of taking an image of a curve about a given line?

The purpose of taking an image of a curve about a given line is to visually represent the relationship between the curve and the line. This can help in understanding the behavior of the curve and its intersection points with the line.

Can you take an image of a curve about a given line on a 3D graph?

Yes, it is possible to take an image of a curve about a given line on a 3D graph. This can be done by using a 3D graphing software or by manually plotting the curve and line on a 3D graph.

How accurate is the image of a curve about a given line?

The accuracy of the image of a curve about a given line depends on the accuracy of the data used to plot the curve and line. If the data is precise, the image will be accurate. However, if the data is not accurate, the image may not accurately represent the curve and line relationship.

Are there any limitations to taking an image of a curve about a given line?

One limitation of taking an image of a curve about a given line is that it may not accurately represent the behavior of the curve and line in all situations. This is because the image is a 2D representation of a 3D concept. Additionally, the accuracy of the image is dependent on the accuracy of the data used to plot the curve and line.

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