Need clarification

Dear Math helpers,

Take a function $f(x)$, for what $x$ is $f(x) = x$? Solve that equation and you're done. i.e: you want to compute the fixed points of $f$, for a sufficiently crude definition of fixed point.

Let's pose $f(x)=x^2-1$.
What the function does basically is it takes elements from the set of $x$ and plugs them in $f(x)$ to output/map as a value in another set.

When you're asked to find elements of the domain that are mapped to themselves, you need to find values of $x$ for which $y=x$.
With $f(x)=x^2-1$, you'd then pose $f(x)=x$.
$x=x^2-1$
$0=x^2-x-1$
$x=-0.618, 1.618$
Hence there are points $(-0.618, -0.618)$ and $(1.618, 1.618)$ on $f(x)$ such that $y=x$.