If f(x) = x x - 1 , then f(a) f(a + 1) = - Vidyadip

MCQ

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

A
$f( - a)$
B
$f\left( {\frac{1}{a}} \right)$
✓
$f({a^2})$
D
$f\left( {\frac{{ - a}}{{a - 1}}} \right)$

✓

Answer

Correct option: C.

$f({a^2})$

c
(c) $\frac{{f(a)}}{{f\,(a + 1)}} = \frac{{a/(a - 1)}}{{(a + 1)/a}} $

$= \frac{{{a^2}}}{{{a^2} - 1}} = f({a^2})$.

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