Question

$f(x) = \frac{x ^{2} + 1}{x { }^{2} - 1} then find f( \frac{1}{2} )$
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Answer 1

Question :-

$\sf{f(x) = \frac{ {x}^{2} + 1}{ {x}^{2} - 1} \: \: then \: find \: f( \frac{1}{2} )}$

Answer :-

$\implies \boxed{ f( \frac{1}{2} ) = - 15} \:$

Explanation :-

Nothing to solve more in this question simply replaced x by 1/2

We have ,

$\implies \sf{ f(x) = \frac{ {x}^{2} + 1 }{ {x}^{2} - 1 } } \\ \therefore \\ \\ \implies \sf{ f( \frac{1}{2}) = \frac{ {( \frac{1}{2} }^{2} ) + 1}{ {( \frac{1}{2}) }^{2} - 1} } \\ \\ \implies \: f( \frac{1}{2} ) = \frac{ \frac{1}{4} + 1}{ \frac{1}{4} - 1} \\ \\ \implies \: f( \frac{1}{2} ) = \frac{ \frac{5}{4} }{ \frac{ - 3}{4} } \\ \\ \implies \boxed{ f( \frac{1}{2} ) = - 15}$

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