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  • If f( x)= y = ax-b/ cx-a then prove that f (y) = x

If f( x)= y = ax-b/ cx-a then prove that f (y) = x

Answers (1)

Given data: f( x)= y = ax-b/ cx-a

Now, let us put x = y in f(x),

 f(y) = ay-b/cy-a

       = \frac{a\frac{\left |ax-b \right |}{\left | cx-a \right |}-b}{c\frac{\left |ax-b \right |}{\left | cx-a \right |}-a}

Thus, f(y) = \frac{a^2x-ab-bcx+ab}{cax-bc-cax+a^2}

                 = \frac{a^2x-bcx}{a^2-bc}

 

           = \frac{x(a^2^-bc)}{a^2-bc}

                =x

Therefore, f(y) = x.

Posted by

infoexpert21

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