What is a even function?
The
equilibrium function is defined as any function in which command f (x) = f (-x) applies to all real x values. The equivalent function is equivalent to any function that is defined for all real X values and has a reflexive symmetry of Y axes. Special or balance of functions is primarily used in graphic functions.
The function is a relationship related to elements from one set of numbers - domains, to elements of another set - range. The relationship is generally defined in terms of the mathematical equation, where if the number is inserted from the domain, the only value of the range is given in response. As an example, for function f (x) = 3x
2 + 1, when x = 2 is a value selected from the domain, f (x) = f (2) = 13.
related to the concept of even function is the odd function. A special feature is the function in whichFunction f (x) = -f (-x) for all real values x. When the graphs are, odd functions have rotating symmetry around origin.
Although most functions are neither special nor even, there are still an endless number of even functions. Constant function, f (x) = C, in which the function has only one value, regardless of which value from the domain is selected, is a even function. Power function, f (x) = e
New even functions can be created from other features that are known to be functions. Adding or multiplying any two even functions creates a new uniform function. If it is evenThe function multiplied by the constant, the resulting function will be even. Even functions can also be made of odd functions. If there are two functions known to be odd, for example f (x) = x and g (x) = sin (x), they will be multiplied together, the resulting function like H (x) = x sin (x) will be even.
New even functions can also be created by composition. The composition function, such as H (x) = g (f (x)), is the one in which the output of one function is used as an input for the other function - G (x). If the most inner function is even, the resulting function will also be regardless of whether the external function is even, odd or neither. For example, the exponential function G (x) =
e x is neither strange nor because the cosine is a uniform function, so the new function H (x) =
One mathematical result claims that each function defined for all real numbers can be expressed as a sum of even and odd functions. If f (x) is defined for VLittle real numbers, it is possible to create two new functions, g (x) = (f (x) + f (-x))/2 and h (x) = (f (x) -f (-x))/2. This implies that G (-x) = (f (-x) + f (x))/2 = (f (x) + f (-x))/2 = g (x), and therefore g (x) is a even function. Similarly, H (-x) = (f (-x) -f (x))/2 =-(f (x) -f (-x))/2 = -h (x), so h (x) is an odd function. If functions are added together, g (x) + h (x) = (f (x) + f (-x))/2 + (f (x) -f (-x))/2 = 2 f (x)/2 = f (x). Each function f (x) is therefore the sum of even and odd functions.