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It is known that f (x) is a function defined on the real number set R and satisfies f (x + 2) - f (x + 2) f (x) - f (x) = 6, f (1) = - 1 / 2, f (2) = - 1 / 4, then f (2006) =?
f(x+2)f(x)+f(x)-f(x+2)+6=0
(f(x+2)+1)(f(x)-1)=7
(f(x+4)+1)(f(x+2)-1)=7
(f(x+4)+1)/(f(x)-1)=1
(f(x+8)+1)/(f(x+4)-1)=1
(f(x+8)+1)*(f(x)-1)=1
(f(x+16)+1)*(f(x+8)-1)=1
(f(x+16)+1)/(f(x)-1))=1
f(x+16)=f(x+4)
f(x+12)=f(x)
f(2006)=f(167*12+2)=f(2)=-1/4
Period: it is known that the function f (x) defined on the set of real numbers on R always satisfies It is known that the function f (x) defined on the real number set on R always satisfies f (x + 2) = - f (x). Judge whether y = f (x) is a periodic function. If so, find one of its cycles
Yeah~
According to the meaning of the question, f (x) = - f (x + 2)
Again, f (x + 4) = - f (x + 2)
The above two formulas can be obtained simultaneously:
f(x)= f(x+4)
So f (x) is a periodic function with a period of 4~
The demand function of goods is p = √ (1000-4q), and find out the Q value to maximize the total income
PQ = q √ (1000-4q), then put the Q square into the root sign, and then match the formulas in the root sign into the mean inequality of the three formulas to obtain the maximum value of the total income, and if and only if 1000-4q = 2q = 2q is an equal sign, that is, when q = 500 / 3, the maximum value is taken
It is known that the demand function is QD = 20-2p, the supply function is equilibrium price and equilibrium quantity QS = 2 + 4P, what are the formats of equilibrium price and equilibrium quantity?
Equilibrium means that supply and demand are equal
Therefore, the equilibrium number and equilibrium quantity can be obtained as long as QD = QS
Thus, 20-2p = 2 + 4P is obtained, P = 3 is obtained, and q = 12 is obtained by substituting it into the expression of QD or QS
That is, the equilibrium price is 3 and the equilibrium quantity is 12
The demand function of a manufacturer is q = 6750-50p, and the total cost function is the square of TC = 12000 + 0.025q
The demand function is q = 6750-50p, so the price function is p = (6750-q) / 50, so the total revenue function is tr = PQ = q (6750-q) / 50, and the known total cost function is TC = 12000 + 0.025q ², When marginal income = marginal cost, i.e. tr ´ = TC ´, the total profit is the largest. [Q (6750-q) / 50] ´ = [
Suppose that the product demand function of a monopoly competition manufacturer is p = 9400-4q and the cost function TC = 4000 + 3000q, find the output, price and profit of the manufacturer at equilibrium
Production according to Mr = MC
MR=9400-8Q MC=3000
9400-8Q=3000 8Q=6400 Q=800 P=9400-4*800=6200
Profit π = tr-tc = pq-4000-3000q = 6200 * 800-4000-3000 * 800 = 2556000
RELATED INFORMATIONS
- 1. The function y = f (x) is an even function on R and an increasing function on (- ∞, 0]. If f (a) ≤ f (2), the value range of real number a is () A. a≤2 B. a≥-2 C. -2≤a≤2 D. A ≤ - 2 or a ≥ 2
- 2. The even function f (x) defined on R monotonically increases in the interval (0, + infinity), and f (2a square + A + 1)
- 3. If the domain of functions f (x) = 3 ^ x + 3 ^ - X and 9 (x) = 3x-3 ^ - x is r, then a, f (x) and 9 (x) are even functions, B, f (x) are even functions, and 9 (x) If the domain of functions f (x) = 3 ^ x + 3 ^ - X and 9 (x) = 3x-3 ^ - x is r, then A, f (x) and 9 (x) are even functions B F (x) is an even function and 9 (x) is an odd function C, f (x) and 9 (x) are odd functions D f (x) is an odd function and 9 (x) is an even function
- 4. A small problem in trigonometric function of senior one mathematics (for finding value range) Known function f (x) = [6 × The fourth power of cosx + 5 × Square - 4] / cos2x of SiNx, find its range Talk about your ideas, (you'd better attach the answer) sin ² We haven't learned the conversion of x = (1-cos2x) / 2. Can you tell me why it is so converted?
- 5. On the maximum value of trigonometric function Just explain how the formula changes Y = maximum value of sinxcosx + cosx + SiNx If it's right, I can add another 50 points Don't use the universal formula. Can you do it with double angle?
- 6. Example 4. It is known that the function y = f (x) is a periodic function defined on R, the period T = 5, and the function y = f (x) (- 1 ≤ x ≤ 1) is an odd function. It is also known that y = f (x) is a primary function on [0,1], a quadratic function on [1,4], and the minimum value of the function is - 5 when x = 2 ① It is proved that f (1) + F (4) = 0; ② Find the analytical formula of y = f (x), X ∈ [1,4]; ③ Find the analytical formula of y = f (x) on [4,9]
- 7. The even function f (x) defined on R is a subtractive function on [0, + ∞), and f (1 / 2) = 0. Then the value range of X with F [Log1 / 4 (x)] > 0 is satisfied
- 8. It is known that the definition domain of function f (x) is x ∈ [- 1] 2，3 2] , find g (x) = f (AX) + F (x a) (a > 0)
- 9. The cost function of a monopoly firm with constant cost is AC = MC = 10 and the market demand function is q = 60-p. (1) find the equilibrium output, price and profit; (2) If the demand function is q = 45-0.5p, find the equilibrium output, price and profit at this time; (3) If the demand function is q = 100-2p, find the equilibrium output, price and profit at this time; (4) This explains why there is no monopoly supply curve
- 10. Let a > 0 and a ≠ 1, then the inverse function of function y = logax and function y = loga1 The image of the inverse function of X (about) A. X-axis symmetry B. Y-axis symmetry C. Y = x symmetry D. Origin symmetry
- 11. It is known that f (x) is an odd function defined on the real number set R, and when x ∈ (0,1), f (x) = 2 ^ X / (4 ^ x + 1) 1. Find the analytical formula of function f (x) on [- 1,1] 2. Judge the monotonicity of F (x) on (0,1) and prove it 3. When t takes what value, the equation f (x) = t has a real number solution on [- 1,1]
- 12. The function f (x) is an odd function defined on R, and when x ∈ (0, + ∞), f (x) = 2x, then f (log21 3)=______．
- 13. Seek the solution process of expanding the function f (x) = (2x + 1) / x ^ 2 + X-2 into a power series of (X-2)
- 14. Given the function f (x) = x ^ 3 + X, the solution set of inequality f (2-x ^ 2) + F (2x + 1) > 0 is
- 15. Application of basic inequalities. Finding the maximum value of function y = (x-1) / (x ^ 2-2x + 10), (x > 1)
- 16. Let f (x) = AX2 + (B-8) x-a-ab, and the solution set of inequality f (x) > 0 is (- 3,2) (1) Find f (x); (2) When the definition field of function f (x) is [0,1], find the value field of function f (x)
- 17. Why does the function f (x) = (2x-x Square) e have a maximum and no minimum
- 18. Suppose the demand function of a commodity is q = 1000-5p, try to find the income function R (q) of the commodity, and find the income when the sales volume is 200 The answer is 32000. I don't know how to calculate it
- 19. The law of diminishing marginal utility is discussed
- 20. Ask for a computational problem in microeconomics A consumer consumes 540 yuan of goods X and Y every year, and the prices of the two goods are 30 and 20 yuan respectively The utility function of is u = XXY, and the quantity of the two commodities purchased each year is calculated