Question

f(x)= x-1/x then number if solutions of f(f(x)=1​

Answer 1

$f(x) = \frac{x - 1}{x} \\ f(f(x)) = \frac{ \frac{x - 1}{x} - 1}{ \frac{x - 1}{x} } \\ f(f(x)) = \frac{ - 1}{x - 1} = 1 \\ x = 0$

Answer 2

$given \: that \: \\ f(x) = x - \frac{1}{x} \\ \\ now \: it \: is \: asked \: for \: f(f(x)) \\ that \:is \: fof(x) \\ fof(x) = (x - \frac{1}{x} ) - \frac{1}{( x - \frac{1}{x}) } \\ simplifying \: it \: we \: get \\ fof(x) = \frac{ {x}^{4} - 3 {x}^{2} + 1}{ {x}^{3} - x } \\ according \: to \: the \: question \\ \\ \frac{ {x}^{4} - 3 {x}^{2} + 1}{ {x}^{3} - x } = \\ this \: is \: 4 \: degree \: equation \: in \: x \: \\ therefore \: x \: will \: have \: total \: of \: fou \: values.$