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Let the piecewise function f (x) = (x-1) ^ 2, when x ≤ 1; 1 / 1-x, when x > 1?
This is a piecewise function, so we must consider the problem of the domain of definition for the outer function, and the domain of definition for the outer function is the domain of the inner function (f (x)), so we need to consider this problem first
Obviously, when x > 1, f (x) = 1 / 1-x < 0, then f (x) must be ≤ 1,
We only need to discuss the problem when f (x) = (x-1) ² ≤ 1, and X ≤ 1. This part is the key to this problem
The solution is 0 ≤ x ≤ 1,
The expression of F (f (x)) is divided into three parts,
When x > 1, f (x) = 1 / (1-x) < 0, then f (f (x)) = (1 / (1-x) - 1) & # 178; = (x / 1-x) & # 178;
When 0 ≤ x ≤ 1, f (x) = (x-1) & # 178; ≤ 1, then f (f (x)) = ((x-1) & # 178; - 1) & # 178; = (X & # 178; - 2x) & # 178;
When x ＜ 0, f (x) = (x-1) & # 178;, then f (f (x) = 1 / (1 - (x-1) & # 178;) = 1 / (2x-x & # 178;)
If the sign Max {x1, X2} denotes the maximum value of X1 and X2, then the minimum value of function f (x) = max {x ^ 2 + 2x-1, x + 1} is_ The increasing interval is
Such as the title
Give an idea, give the best answer
When x ^ 2 + 2x-1 > x + 1, the solution is x1, f (x) = x ^ 2 + 2x-1
So when - 2
If Max {x1, X2} is defined to represent the larger number in x1, X2, then when x ∈ R, the difference between the maximum and minimum value of function f (x) = max {2-x2, X} (where x ∈ [− 3, 13]) is zero______ ．
∵ real number x1, X2, Max {x1, X2} denotes the larger number in x1, X2, ∵ x ∈ [- 3, 13], ∵ for 2-x2, when x = 0, there is a maximum value of 2, when x = - 3, there is a minimum value of - 7, for X, when x = 13, there is a maximum value of 13, when x = - 3, there is a minimum value of - 3, ∵ f (x) = max {2-x2, X} = 2, there is a minimum
If the length of a rectangle can be increased by 2 cm, the area can be increased by 10 square cm; if the length is decreased by 3 cm, a square will be obtained
How many centimeters is the circumference of this rectangle
The length is 8cm, the width is 5cm, and the perimeter is 26cm
How many times does the current direction of a 50 Hz AC change in one second?
50 Hz refers to the frequency of alternating current, that is to say, the direction of alternating current changes every 1 / 50 seconds (0.02 seconds). Because of this, this kind of current is called alternating current. For direct current, the direction of current is constant
1. Make a cuboid oil tank with an iron sheet, measuring 80cm from the inside, 50cm wide and 40cm high. What is the volume of this oil tank?
2. Cut out four squares with sides of 5cm at the four corners of a rectangular sheet iron with length of 60cm and width of 35cm, and then make the remaining sheet iron into a cuboid sheet iron box without cover. What is the volume of this sheet iron box?
1. Make a cuboid oil tank with an iron sheet, measuring 80cm from the inside, 50cm wide and 40cm high. What is the volume of this oil tank?
Volume of oil tank = 80 × 50 × 40 = 160000 cubic centimeter = 160 liter
2. Cut out four squares with sides of 5cm at the four corners of a rectangular sheet iron with length of 60cm and width of 35cm, and then make the remaining sheet iron into a cuboid sheet iron box without cover. What is the volume of this sheet iron box?
The length of rectangular tin box = 60-5-5 = 50cm
The width of the rectangular tin box is 35-5-5 = 25cm
Height of rectangular tin box = 5cm
Cuboid tin box volume = 50 × 25 × 5 = 6250 cm3
The total amount of work is fixed, the working efficiency and working time are closely related______ Proportion
Work efficiency × work time = total amount of work (certain). We can see that work efficiency and work time are two related quantities. Work efficiency changes with the change of work time. Total amount of work is certain, that is, the product of work efficiency and work time is certain, so work efficiency and work time are in inverse proportion
If the side area of a cone is twice of the bottom area, then the degree of the center angle of the sector in the side expanded view of the cone is______ Degree
Let R be the length of generatrix, R be the radius of the bottom, R be the perimeter of the bottom, R be the area of the bottom, R be the area of the side, R be the area of the side, R be the area of the bottom, R be the radius of the bottom, R be the radius of the bottom, R be the perimeter of the bottom, R be the perimeter of the bottom, R be the area of the bottom, R be the area of the side, R be the area of the side, R be the area of the side, R be the radius of the bottom, R be the radius of the bottom, R be the radius of the bottom, R be the radius of the bottom
What must be bigger than what in division with remainder
The divisor must be greater than the remainder
The perimeter ratio of the big circle and the small circle is 6:5. The area of the big circle is 72 square decimeters, and how many square decimeters is the area of the small circle
Jacques 44,
The area ratio is: 6: 178;: 5: 178; = 36: 25
Small circle area: 72 × 25 / 36 = 50 (square decimeter)
RELATED INFORMATIONS
- 1. The minimum value of function y = 1-2 The minimum value of the function y = 1, X2 - 2, x + 6 is__________ The first two is the quadratic velocity of X
- 2. Let f (x) = {- 2x + 1,4x - 5} max, then the minimum value of the function is
- 3. If f (x) is a linear function and 2F (1) + 3f (2) = 3, 2f (- 1) - f (0) = - 1, then f (x) is equal to () A. 4x9+y9B. 36x-9C. 4x9−19D. 9-36x
- 4. Given that the function f (x) satisfies 3f (x) + 2F (- x) = 2x + 2, the analytic expression of F (x) is obtained
- 5. Find the analytic formula 3f (2x-3) + 2F (3-2x) = 2x, f (x) =? I just learned this today, but I don't know much about it Taking this question as an example, I searched the Internet to solve it. The process is as follows: Let 2x-3 = t Then 2x = t + 3 That is, 3f (2x-3) + 2F (3-2x) = 2x 3f（t）+2f（-t）=t+3 ① ∴3f（-t）+2f（t）=-t+3 ② When f (- t) is eliminated, there are two results: ① × 3 - ② × 2 5f（t）=5t+3 ∴f（t）=t+3/5 That is, f (x) = x + 3 / 5 How does the second equation come from,
- 6. Given that a, B and C are three sides of △ ABC, and A2 + B2 + C2 = AB + AC + BC, then △ ABC is () A. Isosceles triangle B. right triangle C. equilateral triangle D. isosceles right triangle
- 7. In the triangle ABC, if cosa = 3 / 5 and Tan (B-A) = 1 / 2, then Tanc
- 8. After a cylinder is cut off 5 cm, the surface area of the cylinder is reduced by 31.4 square cm. What is the volume of the original cylinder?
- 9. Given the function y = Y1 + Y2, and Y1 = 2x + m, y2 = 1-m-1 + 3, the ordinate of the intersection of two function images is 4 1) Finding the functional relation of Y with respect to X
- 10. How much square is 30 cm multiplied by 47 cm
- 11. Hua Luogen said that mathematical analysis should be combined with number and type, and the geometric meaning of partial derivative of binary function should be understood too much in the book
- 12. On the geometric meaning of derivative F (x) = ax ^ 4 + BX ^ 3 + CX ^ 2 + DX + e is even function, passing through point (0, - 1), and the tangent at x = 1 is 2x + Y-2 = 0, Why can we deduce B = 0.d = 0 if f (x) is an even function, and I deduce 2bx ^ 3 + 2DX = 0?
- 13. |What does A-B | mean and its geometric meaning? What if a is - 1 and B is 1
- 14. Three mathematical problems of senior two! The concept of derivative and its geometric significance! Urgent! 1. Y = x ^ 2 + 1, find the slope of the tangent line at point P (1,2) and the equation of the tangent line 2. Given f (x) = x ^ 2, G (x) = x ^ 3, find the value of X suitable for f '(x) + 2 = g' (x) 3. The equation of motion of an object is s (T) = t + 2 / T. The average velocity of the object from t0 to t0 + △ T and the instantaneous velocity at t = t0 are obtained
- 15. Please explain the geometric meaning of gradient
- 16. Prove that the function of two variables is differentiable Let Lim [f (x, y) - f (0,0) + 2x-y] / √ x ^ 2 + y ^ 2 = 0, prove that f (x, y) is differentiable at point (0,0) (x,y)→(0,0) He said: F (x, y) - f (0,0) + 2x-y = O (ρ), (when (x, y) → (0,0)), we can get that f (x, y) is differentiable at point (0,0). How can we get differentiable?
- 17. In binary function, why is there continuous partial derivative and the function is differentiable at a certain point, but the existence of partial derivative is only a necessary condition for differentiability?
- 18. A sufficient condition for differentiability in binary functions, right
- 19. The relationship between derivative and differential, derivative can calculate tangent and slope, so what does differential calculate? indicating contrast
- 20. Differentiation (function) Find d ^ 2Y / DX ^ 2 of each function 1.y=cosx/(√x) 2.x^3-3xy+y^3=4 3.sin y +cos x=1 4.x^2/3+y^2/3=a^2/3 1.1/4x^-5/2[(3-4x^2)cosx +4xsinx] 2.10xy(x-y^2)^-3 3.(cos^2ycos x+sin^2xsin y)/cos^3y 4.(a^2/3)/(3x^4/3 y^1/3)