The function f (x) is known to satisfy f (a + b) = f (a) + F (b) - 6 for any real number a, B ∈ R. when a > 0, f (a)
(1) Let a = - 2, B = 0
We have f (- 2) = f (- 2) + F (0) - 6,
So f (0) = 6
Let a = 2, B = - 2
f(0)=f(2)+f(-2)-6,
So f (2) = 0
(2) Let X1 > x2,
f(X1)=f(X1-X2)+f(X2)-6
f(X1)-f(X2)=f(X1-X2)-6
RELATED INFORMATIONS
- 1. 3. Given that the minimum value of function f (x) = 2sinwx in the interval [- 60 degrees, 45 degrees] is - 2, then the value range of W is? Our teacher gave us two formulas 60 degrees > t / 4 45 degrees > t / 4 T=2π/w But I don't know who can explain
- 2. Find the period, monotone interval, maximum and minimum of the function y = 2Sin (π / 3x-2 / 5 π x), and take the maximum and minimum The set of values of X.
- 3. Find the maximum and minimum values of the function g (x) = 2Sin (x - π / 3) in the interval [0, π] Such as the title
- 4. Find the maximum and minimum value of the function y = - 2Sin (x + π / 6) + 3 in the following interval and the corresponding value of X (1) r, (2) [0, π] (3) [π / 2, π / 2]
- 5. If the even function f (x) defined on R has f (x2) - f (x2) / x2-x1 < 0 for any X1 x2 ∈ [0, + ∞) (x1 is not equal to x2), then a f (3) < f (- 2) < f (1) B F (1) < f (- 2) < f (3) C f (- 2) < f (1) < f (3) d f (3) < f (1) < f (- 2)
- 6. The even function f (x) defined on R satisfies that for any x 1, x 2 belongs to [0, positive infinity] (x 1 ≠ x 2), if (f (x 2) - f (x 1)) / (x 2-x 1), then () A.f(3)<f(-2)<f(1) B.f(1)<f(-2)<f(3) C.f(-2)<f(1)<f(3) D.f(3)<f(1)<f(-2)
- 7. Given the function f (x) = x2-4, if f (- m2-m-1) < f (3), then the value range of real number m is () A. (-2,2)B. (-1,2)C. (-2,1)D. (-1,1)
- 8. Find the necessary and sufficient condition that all the images of the function f (x) = (M2 + 4m-5) x2-4 (m-1) x + 3 are above the x-axis M < 1 or m > 4 1 ≤ m < 19, the intersection should be 4 ≤ m < 19, why not
- 9. Given that the function f (x) = the third power of 1 / 3 * x + the square of M * x, where m is a real number, (1) the tangent slope of function FX at X-1 is 1 / 3, find the value of M, find the process
- 10. Given that the increasing function of function f (x) = x to the second power-2ax-3 is [1, + ∞), then the value of real number a is
- 11. Let f (x) be a function defined on R, if f (0) = 2010, and for any x ∈ R, f (x + 2) - f (x) ≤ 3.2X, f (x + 6) - f (x) ≥ 63.2x, then f (2010)=______ .
- 12. Let x 1x 2 be a quadratic equation of one variable with respect to X. x (square) - 2 (m-1) x + m + 1 = 0. Two real roots are obtained. Y = x 1 + x 2 (both have squares). The analytic trial and range of y = f (m) are obtained
- 13. It is known that the zero point of function f (x) = | X-1 | ^ 3-2 ^ | X-1 | (the intersection of function and X axis) has four X1 x2 x2 x3x4 Then f (x1 + x2 + X3 + x4) =?
- 14. It is known that the zero point of function f (x) = | X-1 | ^ 3-2 ^ | X-1 | (the intersection of function and X axis) has four zeros X1 x2 x2 x3x4 Find f (x1 + x2 + X3 + x4) = how many, do not copy the answer, I want to know how to find the function about where symmetry
- 15. Given the function f (x), for X ∈ R, f (4-x) = f (x). If f (x) has exactly four unequal zeros x1, X2, X3, x4, then X1 + x2 + X3 + X4=
- 16. It is proved that the necessary and sufficient condition for f (x) to be bounded in (a, b) is that f (x) has both upper and lower bounds in (a, b)
- 17. To prove that a function is bounded, must its upper and lower bounds be opposite to each other
- 18. Does bounded function mean that there are both upper and lower bounds in its domain of definition
- 19. It is proved that y = 1-sinx + 7cos3x is a bounded function on its domain
- 20. How to prove that f (x) = √ (x-1) is an increasing function in the domain of definition