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How to judge parity of mathematical function in grade one of senior high school Fast judgment of parity
Use f (- x) to replace all x in the formula, and use - x to replace all x in the formula. If the absolute value and square can not affect the change of X, the final result is f (x) ~ which is even function
If the influence formula cannot be unified with the original formula, then the negative sign is extracted. The formula - f (x) is an odd function. It should be noted that the odd and even function is about (0,0)
Note that symmetric about the y-axis are non odd and non even functions
For the function f (x) defined on R, three propositions are given: (1) if f (- 2) = f (2), then f (x) is even function; (2) if f (- 2) ≠ f (2), then f (x) is not even function; (3) if f (- 2) = f (2), then f (x) must not be odd function______ ．
According to the definition of even function, for any value in the domain of definition, f (- x) = f (x) is satisfied. For ①, only f (- 2) = f (2) is satisfied, which does not mean that it is true for other values on R, so ① is wrong. For ②, the converse proposition is: if f (x) is even function, then f (- 2) = f (2) is true, so
What are the addition, subtraction, multiplication and division of increasing and decreasing functions?
At any time, there is an increase + increase = increase decrease = increase + decrease = decrease increase = decrease. When the function is greater than 0, there is an increase * increase = increase / decrease = increase / decrease * decrease = decrease / increase = decrease. Others cannot be determined
How to judge function parity
In addition to rigorous mathematical reasoning, whether the parity of function can be judged by visual observation. The need of symmetry in Higher Mathematics integral
First of all, the function whose domain is symmetric to the origin may be odd or even. The function whose domain is not symmetric to the origin must be non odd and non even. For example, y = x & # 178; (x-1
Judgment of function parity
For example, f (x) is an odd function, why f (- k * 3 ^ x) = - f (k * 3 ^ x) instead of F (k * 3 ^ (- x)) = - f (k * 3 ^ x)
The definition of odd function is that if f (- x) = - f (x) or F (x) / F (- x) = - 1 for any X in the domain of function f (x), then function f (x) is called odd function
Here x refers to the whole in brackets, not just the letter X on the surface
Personal understanding^_^
To judge the parity of a function, it is necessary to use the process
fx={x^2-2x (x>=0)
x^2+2x (x
A:
X is in the real range R
f(0)=0
When x > 0, - x
The sum of two decimals is exactly the product of their multiplication?
3.5+1.4=3.5×1.4
These two numbers can be 3.5 and 1.4
2.25×1.8=2.25+1.8
These two numbers can also be 2.25 and 1.8
……
There are countless
What is the sum, difference and quotient of an integer added, subtracted and divided by itself equal to 35
Let this number be X
2x+1=35
x=17
A number is added, subtracted, and divided by itself. The sum, difference, and quotient are added again. The sum is 8.6. What is the number?
This number is x; from the meaning of the paper, you can get: (x + X + X + X (x + x) + (x-x-x) + (x-x-x) + (x-x-x-x) + (x-x-x (x-x) + (x-x-x) + (x-x-x) + (x-x-x (x-x-x) + (x-x-x) + (x-x-x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\- 1 = 8.6-1, & nbsp; & nbsp; & nbsp; & nbsp; 2x=7.6， 2x÷2=7.6÷2， &X = 3.8. A: this number is 3.8
RELATED INFORMATIONS
- 1. Given that the function f (x) is equal to {x2-a, X ≥ 0, 2x + 3, x < 0}, if the image of the function f (x) passes through the point (1, - 1) to find The second question about the value of F (f (0)) if the equation f (x) = 4 has a solution, find the value range of A
- 2. Let FX be an increasing function defined on R +, f (x) = f (x / y) + F (y). If f (3) = 1, f (x) - f (1 / X-8) > 2, find the value of X Where > 2 has an equal sign, R + means 0 to positive infinity,
- 3. Let a be greater than 0, f (x) = e ∧ 2 / A + A / E ∧ X be the even function defined on R To prove that f (x) is an increasing function on (0, infinity)
- 4. Given that the zeros of quadratic function f (x) = square of X + MX + n are - 1 and 2, then the solution set of inequality f (x) > 0 is
- 5. Is it necessary to define the partial derivative of a function at a certain point?
- 6. On the concept of function continuity and the problem of limit F (x) = a (x = 1) f (x) = x ^ 3-1 / X-1, (x is not equal to 1) If f (x) is continuous on R, then a is equal to () LIM (an-1 / N + 2A / 3n)= n→∞ robin_ two thousand and six LIM (x → 1) (x ^ 3-1) / (x-1) how to deduce LIM (x → 1) (x ^ 2 + X + 1)
- 7. 1. If the line y = - 2x + 3 intersects the parabola y = ax at two points a and B, and the coordinates of point a are (- 3,9), what are the opening direction, symmetry axis and vertex coordinates? 2. Given that the area of a rectangle is 6, find the functional relation between its length y and width x, and draw the image of this function in rectangular coordinate system 3. The quadratic function y = x-2x + 1 is known (1) Find the vertex a of this function image and the coordinates of its intersection B with y axis (2) Find the coordinates of the intersection points c and D of the function image and X axis; (3) Find ABC of s Triangle 3. The quadratic function y = 1 / 2x & sup2; - 2x + 1 is known (1) Find the coordinates of the vertex a of the function image and its intersection B with the y-axis. (2) Find the coordinates of the intersection points c and D of the function image and X axis; (3) Find ABC of s Triangle
- 8. Simple function problems in senior one According to the previous production and sales experience of a product manufacturer, the following statistical rules about production and sales are obtained: the total cost of each product X (100 sets) is g (x) (10000 yuan), of which the fixed cost is 28000 yuan, and the production cost of each 100 sets is 10000 yuan. The sales income R (x) (10000 yuan) satisfies R (x) = - 0.4x ^ 2 + 4.2x (0 ≤ x ≤ 5) ）11 (x ＞ 5), assuming that the production and marketing of the product are balanced (that is, all the products produced can be sold) (1) Write the analytic formula of profit function y = f (x) (profit = sales revenue total cost) (2) How many products can the factory make the most profit?
- 9. Given the function f (x) = AX2 + BX + C, if f (0) = 0, f (x + 1) = f (x) + X + 1, find the expression of F (x) AX2 is the power of X
- 10. There is a column of numbers arranged from small to large, the minimum number is - 3, and then each number is 2 larger than the previous number, and the maximum number is 155. Note that the nth number is y, and find the analytic expression of Y function on N and the value range of independent variable n. how many numbers are there in this column? (to be specific)
- 11. Are even functions even? If x ^ 2 + B, x + 3 is even, B should be equal to 0 because it is odd Are even functions even? If x ^ 2 + B, x + 3 is even, B must be equal to 0 because it is odd. Then is 3 not odd? Does it become a contradiction between non odd and non even? Does the often said odd and even term mean that the exponent of X is odd or even?
- 12. 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?
- 13. 123456789 the sum of any two numbers is equal to 10, and the multiplication of two numbers is the maximum. What are these two numbers? What is the Enlightenment of this mathematical problem
- 14. Is the absolute value of √ 3 - √ 5 irrational?
- 15. Solve a mathematical factorial sequence sum: ∑ (cos3n) / N! N from 0 to infinity, thank you
- 16. What is the factorial of 1.5 Factorial of 1.5: 1.5? ~ e ~ okay, off?
- 17. Use a circular linked list to represent a polynomial f (x). Please define the node structure of the linked list and write a function value (x), Calculate the value of the polynomial at x = x0
- 18. How many zeros are there at the end of 50! (50! Is read as the factorial of 50, which means 50! = 50 * 49 *... * 3 * 2 * 1)
- 19. Three digit, hundred digit is A-1, ten digit is A-B, one digit is a-b-c, three digit is 210, what's the ABC value Give reasons
- 20. Let f (x) be differentiable at x = A and f '(a) not equal to 0. Find the limit of 1 / x power of [f (a + x) / F (a)] when x tends to 0