Decide the constants so f(x) has got an inverse

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Randyyy

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For what values of a,b and c is [MATH]f(x)=\frac{x-a}{bx-c}[/MATH] its own inverse.
[MATH]x = \frac{y-a}{by-c}[/MATH] and here I am lost. Am I supposed to use the fact that [MATH]f(f^-1(x))=x[/MATH]?
 
[math]xby-xc = y-a[/math]
[math]xby - y = xc-a[/math]
[math]y(bx-1) = xc-a[/math]
[math]y = f^{-1}(x)=\dfrac{xc-a}{bx-1}[/math]
compare to f(x) ...
 
Am I wrong to assume that c=1 then If I compare f(x) to the inverse?
 
to be honest, to me it looks like a and b could be just about any constant and it would work. If not, I have no clue. Maybe I have been staring at the task for too long.
 
Randyyy said:
to be honest, to me it looks like a and b could be just about any constant and it would work. If not, I have no clue. Maybe I have been staring at the task for too long.
Click to expand...
Yes, a and b can be any value. Skeeter was just pointing out that you did not say that. You were asked what a, b and c can be but only mentioned what c can be.
 
Ahhhh, now I feel stupid for having stared at it for 40min and not realizing that it is that simple.. Thanks for the help Jomo and Skeeter!
 
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