For what value(s) of the constant k will the following function not be its own inverse.f(x) =(x - k)/(x - 1)

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For what value(s) of the constant k will the following function not be its own inverse.f(x) =(x - k)/(x - 1)

For what value(s) of the constant k will the following function not be its own inverse.f(x) =(x - k)/(x - 1)
For what value(s) of the constant k will the following function not be its own inverse.
f(x) =(x - k)/(x - 1)

For what value(s) of the constant k will the following function not be its own inverse.f(x) =(x - k)/(x - 1)
题目翻译过来应该是：当常量K取何值时,下列函数的反函数不是它自身?f(x) =(x - k)/(x - 1)
所给函数f（x）自变量的定义域为x≠1
当常量K取1时,原函数等价于f(x)=1 (x≠1) 没有反函数；
当常量K取值不为1时,原函数的反函数求出来仍然是它自身,即f(x) =(x - k)/(x - 1) (x≠1)
所以答案为K=1

这道题目是这个意思
当k取什么值时 f(x)等于他自己的逆函数。
f(x) =(x - k)/(x - 1)
f(x)的逆函数为
y=x-k/x-1
yx-y=x-k
x(y-1)=y-k
x=y-k/y-1
即f-1(x)=(x-k)/(x-1)
所以k=1

y = 1 - (k-1)/(x-1)
(x-1)(y-1)=1-k
so k = 1

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