littleHilbert said:you meant [tex]a + f(x) = - f(-x) - a[/tex], didn't you?
because it must be equivalent to [tex]a + f(x) + a - f(x) = 0 [/tex]
Ok the combination is clear:
[tex]-f(b-x)+a=f(b+x)-a[/tex]
Thank you! :-)
The symmetry of polynomials refers to the property of a polynomial function where its graph remains unchanged when rotated or reflected along a certain axis.
A polynomial is symmetric if it satisfies the condition f(x) = f(-x). This means that if you replace x with -x in the polynomial, it should result in the same expression.
A polynomial can have three types of symmetry: even symmetry, odd symmetry, or neither. Even symmetry exists when a polynomial is symmetric with respect to the y-axis, while odd symmetry exists when a polynomial is symmetric with respect to the origin. A polynomial has neither symmetry when it does not satisfy either of these conditions.
The symmetry of polynomials can be used to simplify equations by reducing the number of terms to be solved. For example, if a polynomial has even symmetry, only the positive values of x need to be considered since the negative values will result in the same expression. This can make solving equations and finding roots easier.
Yes, symmetry of polynomials has various applications in fields such as physics, engineering, and computer graphics. It is used to model and analyze real-world phenomena such as the motion of objects, electrical circuits, and geometric shapes. It is also used in image processing and computer vision to detect and analyze symmetrical patterns.