Question

f(x)=1/1-x,prove that f(f(x))=x​

Answer 1

Step-by-step explanation:

$\underline{ \huge\bf\red{QuestiOn} :}$

$\sf If \: f(x) = \dfrac{1}{1 - x} , then \: prove \: that \: \boxed{ \rm f(f(x)) = \frac{x - 1}{x} }.$

$\underline{ \huge\bf\green{SolutiOn} :}$

We have,

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

Thus,

LHS

$\begin{aligned} \\ & = f( \sf{f(x)}) \\ \\ & = f \left( \frac{1}{1 - x} \right) \\ \\ & = \frac{1}{1 - \dfrac{1}{1 - x} } \\ \\ & = \frac{1}{ \quad \dfrac{(1 - x) - (1)}{1 - x} \quad} \\ \\ & = \frac{1 - x}{ \cancel{1} - x - \cancel{1}} \\ \\ & = \frac{ - (x - 1)}{ - (x)} \\ \\ & = \frac{x - 1}{x} \end{aligned}$

= RHS

$\mid \underline{\underline{\LARGE\bf\green{Brainliest \: Answer}}}\mid$

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