### 二、奇数函数(Odd Function) 1. **定义**:如果对于所有在其定义域内的x值,都有f(-x) = -f(x),则称该函数为奇数函数。 2. **图像特征**:奇数函数的图像关于原点对称。这意味着,如果你画出该函数的图像,并且以原点为中心进行旋转180度,图像的每一部分都会与另一部分完全重合(但方向相反)。 3. **示
The sum of two even functions is even The sum of two odd functions is odd The sum of an even and odd function is neither even nor odd (unless one function is zero).Multiplying:The product of two even functions is an even function. The product of two odd functions is an even function...
Question 1 Supposeg(x)=(x+1)\left(\frac{1}{x}+b\right)wherebis a constant. Findbgiven thatgis an odd function. Question 2 Given thatf(x)is an even function,g(x)is an odd function andf(x)+g(x)=\frac{1}{x-1}, find the expression off(x). Question 3 Supposef(x+y)+f(...
奇函数(odd function),定义为,任意f(x)=-f(-x)的函数,即为奇函数。 偶函数(even function),定义为,任意f(x)=f(-x)的函数,即为偶函数。 奇函数和偶函数在y轴上有一定的对称性。 发布于 2021-06-06 18:20 函数 赞同3添加评论 分享喜欢收藏申请转载 ...
偶函数则定义为对于任意的x，满足f(x) = f(-x)。这意味着对于任何点(x, y)，其关于y轴对称的点(-x, y)也一定在图像上。偶函数的图像通常关于y轴对称。奇函数和偶函数在数学分析和物理学中具有重要应用，特别是在描述对称性、周期性和波动现象时。例如，正弦函数和余弦函数分别属于奇函数和偶...
ODD FUNCTION: f(x) = x3 - 3xf(-x) = (-x)3 - 3(-x) = -x3 + 3x = -(x3 - 3x) Since f(-x) = -f(x) the function is odd. A function can be even, odd or neither even nor odd. To determine if a function has even or odd symmetry use the following guidelines....
The graph of an odd function is the set of points that satisfy the algebraic expression of the function. The left side of the graph is an upside-down version of the right side. What is an odd function? Let y = f(x) be a function. It is odd if it satisfies the property f(-x)...
(–x) =–f(x), then the functionf(x) is said to be odd. For example,y= cosxandy=x2are even functions, andy= sinx, y=x3are odd functions. The graph of an even function is symmetric with respect to they-axis, and the graph of an odd function is symmetric with respect to the ...
Properties OF Even & Odd function & Illustration View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Raja...
An even function is one whose graph exhibits symmetry about the y-axis; an odd function is one whose graph exhibits symmetry about the origin. Which is a fancy way of saying that, if you split the graphs down the middle at the y-axis, an even function's halves will mirror each other...