When a number is added, subtracted and divided by itself, the sum of its sum, difference and quotient is 11.66. What is the number?

(11.66-1) △ 2 = 10.66 △ 2 = 5.33. A: this number is 5.33

The proof of the opposite monotonicity of the symmetric interval of the even function with respect to the origin
The monotonicity of symmetric interval of odd function about origin is the same
How to prove it?

F is even function, f (x) = f (- x)
Let F increase monotonically when x > 0
When 0

Odd functions have the same monotonicity in symmetric monotone interval, even functions have opposite monotonicity in symmetric monotone interval
How to explain this sentence

Because the image of an odd function is symmetric about the center of the origin, its image in a certain interval is obtained by its symmetric interval rotating 180 degrees around the origin, and its monotonicity is of course the same. The image of an even function is symmetric about the y-axis, and its image in the symmetric monotone interval is also symmetric about the y-axis, and its monotonicity is of course the opposite

Is f (x) = x2 + cosx an even function or a non odd non even function

f(-x)=(-x)^2+cos(-x)=x^2+cosx=f(x)
So it's an even function
Upstairs
Cos (- x) = cosx

Is the function f (x) = a ^ (- x) multiplied by (1 + A ^ x) ^ 2 odd or even or not odd or even or odd or even

f(x)=a^(-x)[1+a^(2x)+2a^x]=a^(-x)+a^x+2
Obviously, a is not equal to 0, so it's even

Why do odd and even functions add and subtract to non odd and even functions

Odd function f (- x) = - f (x)
Even function g (- x) = g (x)
Add: F (- x) + G (- x) = - f (x) + G (x)
Not equal to - [f (- x) + G (- x)], so it is not an odd function;
It is not equal to f (- x) + G (- x), so it is not even function
Subtraction is the same

Is the function y = x ^ 4 + 1 / x ^ 2 odd or even, odd or even, non odd or even

Y = x ^ 4 + 1 / x ^ 2 is even function
Because f (- x) = (- x) ^ 4 + 1 / (- x) ^ 2 = x ^ 4 + 1 / x ^ 2 = f (x),
So the function is even

How to see that functions are odd functions, even functions, odd and even functions, and non odd and non even functions

First of all, regardless of odd function or even function, the domain of definition should be symmetric about the Y axis. 1. Look at the image, odd function is symmetric about the origin; even function is symmetric about the Y axis; that is, odd and even function is symmetric about the origin and about the Y axis, this kind of function has only constant function and is 0; non odd and non even function is not symmetric about the origin

What is the difference between non odd and non even functions and functions that are both odd and even? (I forgot...)

Odd function:
f(-x)=-f(x)
Even function:
f(-x)=f(x)
Both odd and even functions:
f(-x)=f(x) and f(-x)=-f(x)
Non odd and non even functions:
There are x0, Y0, such that:
F (- x0) is not equal to f (x0)
F (- Y0) is not equal to - f (Y0)

How to judge non odd and non even functions? Help explain, thank you!

First of all, we need to see whether the domain is symmetric about the origin. If the domain is symmetric, we need to see whether it satisfies f (x) = f (- x) or F (x) = - f (- x). If it does not satisfy both of them, it is a non odd and non even function. If the domain is a point at the origin, it is both an odd function and an even function
To put it simply
f(-x)≠-f(x)
f(-x)≠f(x)
Hope to help you, welcome to ask

When a number is added, subtracted and divided by itself, the sum of its sum, difference and quotient is 11.66. What is the number?