![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
This paper discusses the image relationship between the X-Power of function y = A and the - X-Power of y = a (a > 0 and a is not equal to 1), and proves the symmetry about y wrinkle
Let's look at it another way:
The x power of function y = 2 and the image of function f (x) are symmetrical about the Y axis, then f (x) is equal to?
On Y-axis symmetry
f(-x)=y=2^x=2^[-(-x)]
f(x)=2^-x
The function f (x) = loga (AX-1) (a > 0 and a ≠ 1) is known (I) find the definition domain of F (x); (II) when x is what value, f (x) > 1?
(1) From the meaning of the question, AX-1 > 0, that is, ax > 1 = A0. When 0 < a < 1, x < 0, that is, the definition domain is (- ∞, 0). When a > 1, x > 0, that is, the definition domain is (0, + ∞); (II) from the meaning of the question, loga (AX-1) > 1 = logaa. When 0 < a < 1, 0 < AX-1 < A, then 1 < ax < A + 1, that is, A0
Let f (x) be a continuous function with t as the period, and ∫ (lower limit a, upper limit x) f (T) DT take t as the period, find ∫ (lower limit 0, upper limit t) f (x) DX =?
Let the original function of F (x) be f (x), ∫ (lower limit a, upper limit x) f (T) DT = f (x) - f (a) = f (x + T) - f (a)
F(x+T)=F(x),F(T)=F(0)
∫ (lower limit 0, upper limit t) f (x) DX = f (T) - f (0) = 0
Y = derivative of (3x-5) to the 3rd / 4th power!
3 / 4 times (3x-5) to the (minus 1 / 4) power and then times 3
Given that the cubic power of function f (x) + the quadratic power of 3x - x + 1 is a subtractive function on R, find the value range of real number a
Missing letter A. if f (x) = ax ³＋ 3x ²－ X + 1, then f '(x) = 3ax ²＋ 6x-1 is constant less than or equal to 0 on R, then: a < 0 and the discriminant is less than or equal to 0, so the range of a can be obtained
If the function f (x) is differentiable on the interval [0, a], and f (a) = 0, it is proved that there is at least one point in the interval (0, a) ξ, Make f（ ξ)+ξ f′( ξ)= 0
Construct a new function g (x) = XF (x)
Because g (0) = g (a) = 0
So there must be X
So that G '(x) = 0
RELATED INFORMATIONS
- 1. Let the function f (x) be second-order differentiable on the interval [0,1], and f (0) = 0, f '' (x) > 0. It is proved that f (x) / X is a monotonically increasing function on (0,1]
- 2. It is proved that the function f (x) = LNX / X is an increasing function on (0, e)
- 3. If the function y = f (x) is differentiable in the interval (a, b) and x0 € (a, b), then lim f(x0+h)-f(x0-h)/h h->0 The value of is?
- 4. come Set in (a, b), f '(x) = g' (x), then the following formulas must be true? A.(∫f（x）dx)’=(∫g（x）dx)’ B.∫f’（x）dx=∫g’（x）dx I know a is right, I can't understand it, or B. that expression doesn't make any sense at all?
- 5. Higher number derivative problem (derivative) stem "f (x) = x ^ 3-3ax ^ 2 + 2bx
- 6. What is the geometric meaning of the gradient representation of a binary function? Seeking envelopment····
- 7. If the acceleration direction of the vehicle is consistent with the speed direction, when the acceleration decreases, then () A. The speed of the car also decreases B. The speed of the car first decreases and then increases C. When the acceleration decreases to zero, the car comes to a standstill D. When the acceleration decreases to zero, the speed of the car reaches the maximum
- 8. Using P-Q decomposition method and Newton Raphson method for power flow calculation, which is the faster convergence speed
- 9. Let f (x) be a continuous function and prove that x f (T) (x-t) DT on ∫ lower 0 = ∫ lower 0 and upper x (∫ lower 0 and upper t f (U) Du) DT
- 10. High school physics electromagnetism formula
- 11. Y 'is dy / DX. And y' 'is d ^ 2Y / DX ^ 2. Then why are the [second derivative] obtained by these two methods sometimes different Example 1: it is known that DX / dy = 1 / y '. Why does d ^ 2x / dy ^ 2 = [D (DX / dy) / dy] * DX / dy = - y' '/ y' ^ 3 instead of directly equal to - y '' / y '^ 2? Why does [D (DX / dy) / dy] multiply by DX / dy Example 2: S = asinwt. DS / dt = aw2coswt. D ^ 2S / dt ^ 2 = - aw ^ 2sinwt. How can example 2 not be calculated like example 1 If you know the algorithm of use case 1 and use case 2, please tell us the judgment method,
- 12. The higher number known equation: e ^ y + e ^ (2x) = XY, find the derivative dy / DX of the implicit function determined by the equation
- 13. Given the power of X + 3x + 5 = 7, then the power of X + 3x = (), 3 (power of X + 3x) - 2 = ()
- 14. It is known that f (x) = the x power of 10 plus the x power of 10 / 10 minus the negative x power of 10, Find its value range
- 15. Let the function f (x) = 2 to the power of X / A + A / 2 to the power of X be an even function to find the value of A
- 16. Let a > 0, the x power of F (x) = E / A + the x power of a / E be an odd function. 1. Find a, 2. Prove that it is an increasing function on [0. Positive no group]
- 17. Let the function f (x) be continuous on the interval [a, b], differentiable in (a, b), and ∫ (a, b) f (x) DX = f (b) (B-A). It is proved that there is at least Let the function f (x) be continuous on the interval [a, b], differentiable in (a, b), and ∫ (a, b) f (x) DX = f (b) (B-A). It is proved that there is at least one point in (a, b) ζ, Make f '（ ζ)= 0 Reference. It seems that the teacher said to use the integral mean value theorem first and then Rolle's theorem.
- 18. Let the function f (x) be a function with t as the period, prove that f (AX + b) (A and B are positive numbers) is also a periodic function, and find its period
- 19. F (x) is a function with t as the period. Is the definite integral of F (x) from 0 to a equal to the definite integral of F (x) from t to a + T? Why
- 20. Given that f (x) is an even function, G (x) is an odd function, and f (x) + G (x) = x quartic + 3x-2, find f (x) and G (x)