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On the equation of X: / / X / + A-3 / = a, there are only two solutions. To find the value range of a, note that "/" is the sign of absolute value
a> 1.5 or a = 0 is not necessarily right
|X + 1 | + | 2x-3 | > 4 (remove the sign of absolute value and find the value range of x)
Discuss separately
1. When x > = 3 / 2, x + 1 + 2x-3 > 4 means x > 2, then x > 2
2. When - 1=
Find the maximum value of the function y = (2sinx-1) / (SiNx + 3)
Such as the title
y=（2sinx-1）/（sinx+3）
=(2sinx+6-7)/(sinx+3)
=2-7/(sinx+3)
Because - 1=
Given the square absolute value x + 2a-1 of function f (x) = ax (a is a real constant)
1. If a = 1, find the monotone interval of F (x)
2. If a > 0, the minimum value of F (x) in [1,2] is g (a), find the expression of G (a)
3. Let H (x) = f (x) / x, if the function H (x) is an increasing function in the interval [1,2], find the value range of real number a
Better be more detailed=
F (- 3) = f (1) = 0, so the axis of symmetry is x = 1 / 2 (- 3 + 1) = - 1
Therefore, the original equation can be reduced to f (x) = a (x + 1) ^ 2 + C
Substituting f (1) = 0 into: a (1 + 1) ^ 2 + C = 0
c=-4a
So the original equation is: F (x) = a (x + 1) ^ 2-4a
Substituting f (0) = - 3 into: a-4a = - 3
a=1
So f (x) = (x + 1) ^ 2-4
Then f (x) = 2x
(x+1)^2-4=2x
x^2=3
X = root number 3
Answer: the solution set is x = root number 3
If the image of the quadratic function y = - x2 + MX-1 has two different intersections with the line AB whose two ends are a (0,3), B (3,0), then the value range of M is______ ．
It is known that the equation of line segment AB is y = - x + 3 (0 ≤ x ≤ 3). Because there are two different intersections between quadratic function image and line segment AB, the equations y = − x2 + MX − 1y = − x + 3, 0 ≤ x ≤ 3 have two different real solutions. The elimination result is: X2 - (M + 1) x + 4 = 0 (0 ≤ x ≤ 3), Let f (x) = X2 - (M + 1) x +
Given that the domain of definition of function f (x) is (- 2,2), function g (x) = f (x-1) + F (3-2x). (1) find the domain of definition of G (x) (2) if f (x) is an odd function and monotonically decreasing on the domain, find the inequality g (x)
(1) In order to make g (x) meaningful, then: - 2 ＜ X-1 ＜ 2 (1) - 2 ＜ 3-2x ＜ 2 (2)) from (1), - 1 ＜ x ＜ 3 from (2), 1 / 2 ＜ x ＜ 5 / 2 ‖ 1 / 2 ＜ x ＜ 5 / 2 ‖ g (x) is defined as (1 / 2,5 / 2) (2) g (x) ≤ 0, that is, f (x-1) + F (3-2x) ≤
A math problem - the function of grade one in Senior High School
The value of 1 'formula LG & # 5 + lg2lg50?
2'evaluation: lg5 (LG8 + lg1000) + (LG2 √ & # 179;) &# 178; + LG1 / 6 + lg0.06
lg²5+lg2lg50
=lg²5+lg2（lg5+lg10)
=lg²5+lg2lg5+lg2
=lg5(lg5+lg2)+lg2
=lg5+lg2=1
1. Judge the parity of the function y = x to the second power - 3|x| + quarter (x belongs to real number), and point out its monotone interval
2. Given that the image of quadratic function y = f (x) passes through the origin, and f (x-1) = f (x) + X-1, find the expression of F (x)
1、
f(-x)=(-x)²-3|-x|+1/4=x²-3|x|+1/4=f(x)
The domain of definition is r, symmetric about the origin, so it's an even function
x>0,f(x)=x²-3x+1/4=(x-3/2)²-2
Opening up, so 0
1. Given that the domain of function f (x) is (1,3), what is the domain of function y = f (x-1) + F (4-x)
2. Let f (x) be a linear function and f [f (x)] = 4x + 3, then f (x) =?
1: The domain is (1,3)
2: Let f (x) = ax + B
=>f(f(x))=a*a*x+ab+b=4x+3
=>F (x) = 2x + 1 or F (x) = - 2x-3
1. If the domain of function y = f (x) is [0,1], then the domain of function f (x) = f (x + a) + F (2x + a) (0 < a < 1) is?
2. Given the function f (x) = 1 / 2x & sup2; - x + 3 / 2, whether there is a real number m, so that the domain of definition and range of value of the function are [1, M] (M > 1)? If there is, find the value of M; if not, explain the reason
1 [-a/2,(1-a)/2]
2 F (x) = (x-1) ^ 2 / 2 + 3 / 2 when x > 1, f (x) increases monotonically
When the domain is [1, M], the maximum value is obtained when x = m, because the domain is also [1, M]
So m = f (m), substituting M = 1 / 2m ^ 2-m + 3 / 2
The solution is m = 1,3 (M > 1)
So m = 3
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- 6. When n is a positive integer, the function n (n) represents the largest odd factor of n When n is a positive integer, the function n (n) represents the largest odd factor of N, such as n (3) = 3, n (10) = 5, Let Sn = n (1) + n (2) + n (3) + n (4) +... + n (the nth power of 2) + n (the nth power of 2) The answer is (n power of 4 + 2) / 3,
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- 13. The value range of function y = ln (AX ^ 2 + ax + 1) is all real numbers, and the value range of real number a is calculated
- 14. Function f (x) = ln (a + 2 / x + 1) the image is symmetric about the origin, which a =?
- 15. Let f (x) = ln (x − 1) + 2aX (a ∈ R) (1) find the monotone interval of F (x); (2) if ln (x − 1) x − 2 > ax is constant when x ＞ 1 and X ≠ 2, then find the value range of real number a
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- 19. The maximum value of the function y = 2x ^ - 2 in the interval [1,3] is_____
- 20. It is known that the functions y = ax and y = - BX are decreasing functions in the interval (0, + ∞). Try to determine the monotone interval of the function y = AX3 + bx2 + 5