The known function f (x) = a − x If the symmetry center of the inverse function image of X − a − 1 is (- 1,3), then the value of real number a is () A. 2 B. 3 C. -3 D. -4

The known function f (x) = a − x If the symmetry center of the inverse function image of X − a − 1 is (- 1,3), then the value of real number a is () A. 2 B. 3 C. -3 D. -4

The function f (x) = a − x
The symmetry center of the inverse function image of X − a − 1 is (- 1,3), so the symmetry center of the original function is (3, - 1),
The function is f (x) = a − X
x−a−1＝−1+−1
X − a − 1, so a + 1 = 3, so a = 2
Therefore, a

If the symmetric center of the image of the inverse function F-1 (x) of the function f (x) = (A-X) / (x-a-1) is known to be (B, 3), then a + B is a real number

Because f (x) = - 1 - 1 x-a-1, let y '= y + 1, X' = x-a-1, y '= - 1 x' is an inverse proportional function and is an odd function, then the center of symmetry is (0,0), that is, y '= 0, X' = 0, y = - 1, x = a + 1, so the symmetry center of function y is (a + 1, - 1) according to the symmetry of the images of reciprocal functions with respect to y = x, the inverse function F-1 is obtained

The function f (x) = a − x If the symmetry center of the image of the inverse function F-1 (x) of X − a − 1 is (- 1,3), then the real number a=______ .

∵ the symmetry center of the image of the inverse function F-1 (x) of the function f (x) = a − XX − a − 1 is (- 1,3),  f (x) is (3, - 1), y = f (x) = a − XX − a − 1 = - x − a − 1 + 1x − 1 = - 1x − (a + 1) − 1,

If the symmetric center of the image of the inverse function f - (x) of the function f (x) = A-X / x-a-1 is (- 1,3 / 2), then the value of real number a is

The inverse function is obtained by F (x) = (A-X) / (x-a-1), because f (x) = (A-X) / (x-a-1) = - (x-a-1 + 1) / (x-a-1) = - 1-1 / (x-a-1)
So its inverse function is f (x) = - 1 / (x + 1) + A + 1. Because the symmetry center of the image of the inverse function f (x) is (- 1,3 / 2), there is a + 1 = 3 / 2
So a = 1 / 2

The function f (x) = a − x If the symmetry center of the image of the inverse function F-1 (x) of X − a − 1 is (- 1,3), then the real number a=______ .

The function − a ∵
The symmetry center of the image of the inverse function F-1 (x) of X − a − 1 is (- 1,3),
The center of symmetry of F (x) is (3, - 1),
y=f(x)＝a−x
x−a−1
=-x−a−1+1
x−a−1
=-1
x−(a+1)−1，
∴y+1=-1
X − (a + 1) is a hyperbola,
The center of hyperbola is known as 3 - (a + 1) = 0
A = 2
So the answer is: a = 2

Given the function f (x) = loga (AX radical x)) (a > 0, a is not equal to 1 is a constant) (1) find the definition domain of function f (x) 1) Find the definition domain of function f (x) (2) if a = 2, try to determine the monotonicity of function f (x) according to the definition of monotonicity. (3) function y = f (x) is an increasing function, and find the value range of A

1. Let x = t (T > 0)
F = loga (at ^ 2-At), to find the definition field is to ensure that at ^ 2-At > 0, because a > 0, that is, T ^ 2-T > 0, is transformed into a quadratic function about t, whose range is > 0, t > 1
2. A = 2, f = log2 (2t ^ 2-2t). First of all, note that the definition domain is t > 1, then the logarithmic function is meaningful
Then, because the outer function increases, the monotonicity of the whole function is consistent with the monotonicity of the quadratic function
Because the quadratic function increases, so f increases the function
3. There are two cases of F increase
1)01

The function f (x) = loga (2x-1) (a > 0 and a ≠ 1) is known, (1) Find the definition domain of F (x) function; (2) Find the value range of X for f (x) > 0

(1) ∵ 2x-1 ᦝ 0, ᙽ 2x ᙽ 1 = 20, ᙽ f (x) = 2x is an increasing function on R,

Given that f (x) = loga radical, 2-2x (a is greater than 0 and a is not equal to 1) (1) find the definition domain of function f (x) Given that f (x) = loga radical, 2-2x (a is greater than 0 and a is not equal to 1) (1) find the definition domain of function f (x) (2) find the value range of X of F (x) > 0

Define the domain as X

Given the function f (x) = loga (a ^ x-1), (a > 0, and a is not equal to 1), find the domain of F (x) and monotonicity of F (x) 1. Find the domain of F (x), 2. Monotonicity of F (x) 3.f(2x)=f^-1(x)

First find the definition field a ^ X-1 > 0 a ^ x > A ^ 0
When a > 1, the definition domain x > 0
In this case, u = u = u is a composite function with the original function
The former is an increasing function, the latter is also an increasing function (a > 1), and monotonic composition is also an increasing function
Zero

If the function y = f (x) is the inverse function of the function y = ax (a > 0 and a ≠ 1), its image passes through a point（ a. A), then f (x) =___ .

The inverse function of ∵ function y = ax is f (x) = logax（
a，a），
∴a=loga
a. That is, a = 1
2，
So the answer is: Log1
2x．