If the image of function f (x) = (1-ax) / (1 + ax) (x is not equal to 1 / a) is symmetric with respect to y = x, then what is a?

First of all, it is difficult to determine if the following question is y = (1-ax) / (1 + ax) without clear brackets. Secondly, it is necessary to make clear that the image of the original function and the inverse function is symmetrical about the straight line y = x, so the original function of this function is equal to the inverse function. Find the inverse function: y = (1-ax) / (1 + ax) (1 + ax) y = 1-ax, y + AX = 1-ax, ax + AX = 1

If the image of function f (x) = ax + 2 / X-1 is symmetric with respect to the line y = x, then a=

y=（ax+2）/（x-1）
xy-y=ax+2
（y-a）x=y+2（1）
Because it's symmetric about y = X
that
x=（ay+2）/（y-1）
xy-x=ay+2
（y-1）x=ay+2（2）
According to (1) (2)
So a = 1

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