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The only way a function can be both even and odd is for it to ignore the input, i.e. for it to be a constant function. e.g. f(x)=4 is both even and odd.
An even function is one where f(x)=f(-x), and an odd one is where -f(x)=f(-x).
This doesn't make sense. Let's analyze.
For a function to be even, f(-x)=f(x). For a function to be odd, f(-x)=-f(x).
In this case, f(x)=4, and f(-x)=4. As such, for the first part of the even-odd definition, we have 4=4, which is true, making the function even. However, for the second part of it, we have 4=-4 (f(-x)=4, but -f(x)=-4), which is not true. Therefore constant functions are even because f(-x)=f(x), but not odd because f(-x)!=-f(x).
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Is the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
Is there a function that is both even and odd?
Yes f(x)=0 is both even and odd
Is f of x equal to negative x an even or odd function?
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
Can a function be both even and odd functions?
yes
Why you use even and odd function in mathematics?
If you know that a function is even (or odd), it may simplify the analysis of the function, for several purposes. One example is the calculation of definite integrals: for an odd function, the integral of a function from (-x) to (x) (note 1) is zero; for an even function, this integral is twice the integral of the function from (0) to (x). Note 1: That is, the area under the function; for negative values, this "area" is taken as negative) is
What are even and odd functions?
An even function is a function that creates symmetry across the y-axis. An odd function is a function that creates origin symmetry.
Why is the secant function is an even function and the tangent and cosecant are odd functions?
I find it convenient to express other trigonometric functions in terms of sine and cosine - that tends to simplify things. The secant function is even because it is the reciprocal of the cosine function, which is even. The tangent function is the sine divided by the cosine - an odd function divided by an even function. Therefore it is odd. The cosecant is the reciprocal of an odd function, so it is naturally also an odd function.
What is the difference of odd and even functions?
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
Is signum function an odd or even function?
both
Is the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
Is there a function that is both even and odd?
Yes f(x)=0 is both even and odd
Can a function be odd and even?
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2. A function can be either.
What is the composition of an even and an odd function?
For an even function, f(-x) = f(x) for all x. For an odd function, f(-x) = -f(x) for all x.
Is A function with a graph that is symmetric about the origin an even function?
An even function is symmetric about the y-axis. If a function is symmetric about the origin, it is odd.
How do you determine if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
How do you tell if a function is even or odd?
You can tell if a function is even or odd by looking at its graph. If a function has rotational symmetry about the origin (meaning it can be rotated 180 degrees about the origin and remain the same function) it is an odd function. f(-x)=-f(x) An example of an odd function is the parent sine function: y=sinx If a function has symmetry about the y-axis (meaning it can be reflected across the y-axis to produce the same image) it is an even function. f(x)=f(-x) An example of an even function is the parent quadratic function: y=x2
Is f of x equal to negative x an even or odd function?
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
