Question

If y=f(x)=6x-5/5x-6, then prove that f(y)=x.​

Answer 1

Step-by-step explanation:

$y = f(x) \\ f(y) = f(f(x)) = \frac{6( \frac{6x - 5}{5x - 6}) - 5 }{5 (\frac{6x - 5}{5x - 6}) - 6} \\ = \frac{ \frac{(6(6x - 5) - 5(5x - 6)}{(5x - 6)} }{ \frac{5(6x - 5) - 6(5x - 6)}{(5x - 6)}} \\ = \frac{36x - 30 - 25x + 30}{30x - 25 - 30x + 36} \\ = \frac{9x}{9} = x$

$hence \: f(y) = f(f(x)) = x$