If f(x) = (1-x)
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x
what is f(f(x))
please could you explain it too? I have no idea whatsoever what I'm doing.
here is how function notations work. whatever shows up in the brackets, you replace x with it (or whatever variable the function is defined for)
example: if $\displaystyle g(x) = x^2 + 2x + 3$
then, $\displaystyle g(1) = (1)^2 + 2(1) + 3 = 6$ ..........i replaced x with 1
$\displaystyle g(3) = (3)^2 + 2(3) + 3 = $ ..................i replaced x with 3
$\displaystyle g($ $\displaystyle ) = ($ $\displaystyle )^2 + 2($ $\displaystyle ) + 3$ ...............i replaced x with ....(assume is in the domain of g(x) )
what if we had another function?
$\displaystyle h(x) = x + 1$
then, $\displaystyle g(h(x)) = (h(x))^2 + 2(h(x)) + 3 = (x + 1)^2 + 2(x + 1) + 3$ ...........i replaced the x in g(x) with h(x)
and
$\displaystyle h(g(x)) = (g(x)) + 1 = (x^2 + 2x + 3) + 1 = x^2 + 2x + 4$ ............i replaced the x in h(x) with g(x)
now, can you do your problem?