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It is known that the function f (x) is an odd function defined on R. when x is greater than or equal to 0, f (x) = x (1 + x). The image of function f (x) is drawn and the analytic formula of the function is obtained
When x is less than 0, - x > 0, f (- x) = - x (1-x)
Because the function f (x) is an odd function over R, f (- x) = - f (x) = - x (1-x)
So f (x) = x (1-x)
So: X
As a function of y = 2x-1, what value of X is, when y > 5x, y is less than or equal to - 3, why x is, y = - 7
Solve three inequalities, one, two X-1 > 5x has X
When x is equal to, the value of function y = 5x + 3 is greater than 0, and when x is equal to, the value of function y = 5x + 4 is less than 0
When x > - 3 / 5
The value of y = 5x + 3 is greater than 0
When x < - 4 / 5
The value of y = 5x + 4 is less than 0
It is known that y = f (x) is a function defined on R, and its image is symmetric with respect to x = 2. When x is greater than or equal to zero, f (x) = 5x + 3
Is the title wrong
When x is greater than or equal to 2, f (x) = 5x + 3,
X2
f(x)=f(4-x)=5(4-x)+3=-5x+23
Make the image of function y = 0.5x-4, and answer the question according to the image: 1. When x takes what value, y is greater than 0? When - 1 is less than or equal to X and less than or equal to 2, find the range of Y
The function image is a straight line, which intersects with y axis at (0, - 4) and X axis at (8,0)
When x > 8, Y > 0
When - 1 is less than or equal to X and less than or equal to 2, - 11 / 2
Draw the graph of the function y = | X-1 | + | 2x + 3 |, and write its monotone interval and maximum value according to the image
You just need to change this function into a piecewise function. When x is greater than 1, when x is less than or equal to 1 and greater than or equal to - 2 / 3, and when x is less than - 2 / 3, we will discuss it in three paragraphs
Write the monotone interval of the function y = x? - 2x and the symmetry axis of the image. Observe: what are the characteristics on both sides of the function image
y = x² - 2x = (x - 1)² - 1
The monotone decreasing interval of function y is (- ∞, 1), and the monotone increasing interval is [1, + ∞)
The symmetry axis is x = 1. It is observed that the function values of the function image are equal on both sides of the symmetry axis
The graph of the function y = x? - 4|x | - 5 is made, and the monotone interval of the function is written
X>0
y=x²-4x-5=(x-2)²-9
X<0
y=x²+4x-5=(x+2)²-9
X=0
y=-5
X < - 2 minus
-2 < x < 0
0 < x < 2 decreased
x> 2
Let f (x) and G (x) = Log1 If the graph of 2x is symmetric with respect to the straight line y = x, then the monotone increasing interval of the function f (x2 + 2x) is______ .
∵ function f (x) and function g (x) = Log1
The image of 2x is symmetric about the line y = X,
∴f（x）=(1
2) x
The function f (x) decreases monotonically on R
∵t=x2+2x=（x+1）2-1，
ν t = x2 + 2x decreases monotonically on (- ∞, - 1]
The monotonic increasing interval of function f (x2 + 2x) is (- ∞, - 1]
So the answer is: (- ∞, - 1]
It is proved that the function f (x) = x 2 is an increasing function on the interval [0, + ∞) Ask for the great God sect
It is proved that: F (x) = x 2, let X1 > x2 > = 0f (x1) - f (x2) = X1? - x2 = (x1-x2) (x1 + x2) because: X1 > x2 > = 0, so: x1-x2 > 0, X1 + x2 > 0, so: F (x1) - f (x2) = (x1-x2) (x1 + x2) > 0, so: F (x1) > F (x2) so: F (x) = x ~ 2 is increasing in the interval [0, + ∞)
RELATED INFORMATIONS
- 1. It is proved that the function y = - x 2 + 3 increases monotonically on the interval (- ∞, 0)
- 2. Find the monotone interval of the function y = 2Sin (2x - sextuple) + 1, the symmetry center and symmetry axis equation of an image
- 3. If the symmetric axis of the function y = 2Sin (3x + a) (| a | x < π / 2) is x = π / 12, then a =?
- 4. How to find the period of F (x) = 2Sin ^ 2-2 radical 3 * SiNx * cosx + 1 As in the title,
- 5. Let f (x) = root sign 3sinxcosx + cos ^ 2 + m, where m is a constant (1). Find the minimum positive period of F (x) (2) let a = {x | π / 6 ≤ x ≤ π / 3}. We know that the minimum value of F (x) is 2 when x ∈ a, and the maximum value of F (x) when x ∈ a
- 6. F (x) = the square of 2Sin X - (cosx SiNx) to find the monotone decreasing interval of this function
- 7. Function y = lgsinx+ cosx−1 The domain of 2 is______ .
- 8. If the definition field of (a - | x-4 |) under f (x) = 1 / radical is a non empty set a, the definition domain of function g (x) = under radical sign [(2 - (x + 3 / x + 1)] is B, if a intersects B = a, find the value of A
- 9. The definition domain of the function f (x) = the square of 1-x under the root sign + the square of X under the root sign is
- 10. Find the definition domain of X-1 under the function f (x) = LG (x + 2) / radical
- 11. The image of function y = Tan absolute value x is made, and the parity, periodicity and monotone interval of this function are judged according to the image
- 12. Periodic maximum monotone interval y = sin (2x + π / 3) y = 2Sin (2x + π / 6) - 2 y = sin (π / 3-2x) y = Tan (π / 3-2x)
- 13. The maximum value of y = sin ^ 2x + sinxcosx + 3cos ^ 2x
- 14. If there is a common point between the straight line y = 3 / 4x + B and the curve y = root sign (4x-x Square), then the value range of B is to explain how to draw the semicircle under y = root sign (4x-x Square)?
- 15. If the line y = KX + 4 + 2k and the curve y= If 4-x2 has two intersections, then the value range of K is______ .
- 16. If the straight line x + y = K and the curve y = radical 1-x ^ 2 have exactly one common point, then the value range of K is? RT see that it is not the previous one, please do not copy and paste. Thank you
- 17. If the absolute value of the radical X-1 + Y-3 = 0, what is the equivalent of X * XY / 2Y
- 18. What is the curve represented by the equation | X-1 | = root sign (1 - (Y-1) ^ 2)?
- 19. F (x) = 2 radical 3sin (ω x + π / 3) (ω > 0), f (x + θ) is an even function with period 2 π (1) Find the value of ω and θ (2) When x ∈ [- π / 2, π / 12], find the range of F (x)
- 20. It is known that the minimum positive period of the function y = radical 3sinwxcoswx cos ^ 2wx + 3 / 2, (x ∈ R, w ∈ R) is π, and when x = π / 6, the function has a minimum value, (1) find the analytic formula of F (x), and (2) find the monotone increasing interval of F (x)