Under what conditions the function
y =(ax+b)/(cx+d), (ad- bc)not= 0 is it’s own inverse?

Question

Under what conditions the function y =(ax+b)/(cx+d), (ad- bc)not= 0 is it’s own inverse?

bharat bajaj · Answer

First inverse the function :
x = ay + b / cy + d
xcy + dx = ay + by = b - dx/ cx - a
It should be equal to original function
b - dx/ cx - a = ax + b/cx + d
bcx + bd - dcx^2 - d^2x = acx^2 + bcx - a^2x - ab

By this, we get a = -d should be the other condition.
Thanks
Bharat
askiitians faculty
IIT Delhi

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Under what conditions the function y =(ax+b)/(cx+d), (ad- bc)not= 0 is it’s own inverse?

Under what conditions the function
y =(ax+b)/(cx+d), (ad- bc)not= 0 is it’s own inverse?

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