Question 911269
Attempting just to find a formula for the inverse, {{{f^-1(x)=(x-k)/(x-1)}}} as expected.


Look at the function definition.  
x<>1 because f is undefined there.
x=0 makes for f=k, a constant.
x=k makes f=0.
We want to know a certain value for k so that f has either a different inverse or has no inverse.


k=0, f is just a more specific function.
k=1, then {{{f(k)=f(1)=1}}}, which is a constant.


For {{{highlight(k=1)}}}, f will be the line {{{f(x)=1}}}, a HORIZONTAL LINE, the same "y" for all values of x.  If  you reflect this over the line {{{y=x}}}, this forms the inverse RELATION, {{{x=1}}}.  This is NOT a function; because it is a VERTICAL LINE, and has infinite values of y for just one value of x.


<i>For what value(s) will the constant k will the following function NOT be it's own inverse?</i>


ANSWER:   {{{highlight(k=1)}}}.