Question

if $f(x)= x - \frac{1}{x}$ , then find the value of $f(f(\frac{1}{x}))$. kindly help, relations and functions class 11

Answer 1

Answer:

$f(f( \frac{1}{x} )) = \frac{ {x}^{4} - 3 {x}^{2} + 1 }{x(1 - {x}^{2} )}$

Step-by-step explanation:

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

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

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

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

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

$f(f( \frac{1}{x})) = \frac{1 + {x}^{4} - 2 {x}^{2} - {x}^{2} }{x(1 - {x}^{2} )}$

$f(f( \frac{1}{x})) = \frac{ {x}^{4} - 3 {x}^{2} + 1 }{x(1 - {x}^{2} )}$

Hope it helps you. If still you have any query about relations and functions or anything in mathematics, feel free to ask me.