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raja kapoor Grade:
        

Hi ,


Show that the inverse of a linear fraction function is always a linear fraction function (except where it is not defined).

8 years ago

Answers : (1)

vivek gupta
26 Points
										

Let, f(x) = (a+bx)/(c+dx) be the said linear fraction function.


Let at some x it attains value y, so,


                 (a+bx)/(c+dx) = y


                => a + bx - cy - dxy = 0


                => a - cy + x (b - dy) = 0


                => x = (cy-a)/(b-dy).


Which is again a linear fraction function defined in R except


                 at x = -c/d and y = b/d


and inverse of the given function is, y = (cx-a)/(b-dx).


 

8 years ago
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