If the image of function f (x) = ax + 1 / X-1 is symmetric with respect to the line y = x, then a=

If the image of function f (x) = ax + 1 / X-1 is symmetric with respect to the line y = x, then a=

The image of the function y = (AX + 1) / (x-1) is symmetric with respect to the line y = X,
Then the positions of X and y can be interchanged: x = (ay + 1) / (Y-1), and the arrangement is: y = (x + 1) / (x-a),
Compared with the original formula, a = 1

]Given the power function y = f (x) of the image through (2, root 2), try to find the analytic formula and properties
Given the image process (2, root 2) of power function y = f (x), try to find the analytic formula and properties
hard

Because it is a power function, it must be written as y = f (x) = x ^ a
It is known that: √ 2 = 2 ^ a
The solution is a = 1 / 2
So y = f (x) = √ X
Property: domain: X ≥ 0, monotonically increasing on the domain

It is known that the minimum positive period of the function f (x) = sin (Wx + π / 4) (W > 0, X ∈ R) is half π
The analytic expression of F (x) by 1
2 set 0

The minimum positive period of F (x) = sin (Wx + π / 4) is π / 2, and 2 π / w = π / 2, w = 4,
Then the function y = f (x) = sin (4x + π / 4)
0