Question

4. If f(x)= x/x-1 ,x ne1
(a) Find fof * (x)
(b) Find the inverse of f

Answer 1

Step-by-step explanation:

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

a)

$fof(x) = f(f(x))$

$= > fof(x) = \frac{ \frac{x}{x - 1} }{ \frac{x}{x - 1} - 1 }$

$= > \frac{ \frac{x}{x - 1} }{ \frac{x - x + 1}{x - 1} } = > \frac{ \frac{x}{x - 1} }{ \frac{1}{x - 1} } = > x$

Therefore,

$fof(x) = x$

b)

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

$let \: y = f(x)$

$= > y = \frac{x}{x - 1}$

$= > y(x - 1) = x$

$= > yx - y = x$

$= > yx - x = y$

$= > x(y - 1) = y$

$= > x = \frac{y}{y - 1}$

$let \: g(x) \: be \: the \: inverse \: of \: f(x)$

$= > if \: f(x) = y \: then \: g(y) = x$

$substituting \: x \: as \: x = \frac{y}{y - 1}$

$= > g(y) = \frac{y}{y - 1}$

$= > g(x) = \frac{x}{x - 1}$

Therefore,

$inverse \: of \: f(x) = \frac{x}{x - 1}$

Hope this helps!

Answer 2

Answer:

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