Question:
If $f(x)=\frac{x}{x-1}=\frac{1}{y}$, then $f(y)=$ _____________ .
Solution:
$f(x)=\frac{x}{x-1}$
given $\frac{x}{x-1}=\frac{1}{y}$
$x y=x-1 \quad$ i.e $y=\frac{x-1}{x}$
i. e $f(y)=\frac{y}{y-1}$
$=\frac{\frac{x-1}{x}}{\frac{x-1}{x}-1}$
$=\frac{\frac{x-1}{x}}{\frac{x-1-x}{x}}$
$=\frac{x-1}{x} \times \frac{x}{-1}$
$=-(x-1)$
$\therefore f(y)=1-x$
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