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Find the [(2x + 1) / (x-1) power of the definition field and value field F (x) = 3 of the function Because 3 / X-1 belongs to R, all values are not equal to 0 What do you mean? Analyze it in detail and the one behind it
You see, let X-1 = T.T belong to R, so the value range of 3 / T is (- infinity, 0) and up (0, positive infinity). You can imagine the 1 / X image. As long as X ≠ 1, 2x + 1 / X-1 = 2x-2 + 3 / X-1 = 2 + 3 / (x-1) because 3 / X-1 belongs to R, all values are not equal to 0, so 2x + 1 / X-1 belongs to - infinity, 2 and 2, positive
Find the definition field, value field and monotone interval of function y = log2 (x2-6x + 5)
To make the function meaningful, then x2-6x + 5 > 0, the solution is x > 5 or x < 1, that is, the definition domain of the function is {x | x > 5 or x < 1}. Let t = f (x) = x2-6x + 5 = (x-3) 2-4, ∵ x > 5 or x < 1,
The function y = f (x) is the subtraction function on the definition field R, then the monotone subtraction interval of function f (｜ x + 2 ｜) is
x>-2
The function y = f (x) is a subtraction function over the definition field R
And the monotone decreasing interval of F (｜ x + 2 ｜), then ｜ x + 2 ｜ is an increasing function in this interval, so x > - 2
Given y = f (|x-2|), if y = f (x) is a subtractive function in the definition field R, the monotone subtractive interval of function y = f (|x-2|) is What is the specific and detailed method of [same increase and different decrease]?
Y = f (x) as an external function is a subtractive function
According to the same increase and difference decrease
When | X-2 | increases, y = f (| X-2 |) decreases
|The increasing interval of X-2 | is [2, positive infinity)
So the subtraction interval of y = f (|x-2|) is [2, positive infinity)
Function f (x + 1) = x2_ 2x+1=x2_ The domain of 2x + 1 is negative two to zero. Then what is the monotonic decreasing interval of the equation about x?
f(x+1)=x2-2x+1
f(x+1)=(x+1)^2-4(x+1)+4
f(x)=x^2-4x+4
-2-3 axis of symmetry of curve: x = 2, opening upward
-1 so,
The decreasing range is: - 3 to - 1
If the domain of function f (x + 1) = x2-2x + 1 is [- 2, 6], then the monotonic decreasing interval ____ of function y = f (x)
∵ the definition field of function f (x + 1) = x2-2x + 1 is [- 2, 6], ∵ - 2 ≤ x ≤ 6, ∵ - 1 ≤ x + 1 ≤ 7
Let x + 1 = t, then x = T-1, and - 1 ≤ t ≤ 7,
∴f（t）=（t-1）2-2（t-1）+1=（t-2）2，
The monotonic decreasing interval of function y = f (x) is [- 1, 2]
So the answer is [- 1, 2]
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