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Can a function be both even and odd functions?
yes
What is the function that is both even and odd?
f(x) = 0
Is fx equals c an even or odd function?
Even (unless c = 0 in which case it is either or both!)
How a function is even and odd?
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).
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 signum function an odd or even function?
both
Can a function be both even and odd functions?
yes
What is the function that is both even and odd?
f(x) = 0
Can a function be both even and odd?
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.
Is fx equals c an even or odd function?
Even (unless c = 0 in which case it is either or both!)
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.
How a function is even and odd?
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).
Is the sine functions an odd function?
Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.
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.
