If f(x) = x x - 1 = 1 y , then f(y) = - Vidyadip

MCQ

If $f(x) = \frac{x}{{x - 1}} = \frac{1}{y}$, then $f(y) = $

A
$x$
B
$x + 1$
C
$x - 1$
✓
$1 - x$

✓

Answer

Correct option: D.

$1 - x$

d
(d) $f(x) = \frac{x}{{x - 1}} = \frac{1}{y}\,\, $

$\Rightarrow \,\,\frac{{ - 1}}{{x - 1}} = \frac{{y - 1}}{y}$ {Applying dividendo}

$ \Rightarrow \,\,\frac{{x - 1}}{{ - 1}} = \frac{y}{{y - 1}}\, $

$\Rightarrow \,\, - x + 1 = f(y).$

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