## Thomas' Calculus 13th Edition

$f(g(x))=\sqrt[4] {1-x}$, Domain $(-\infty,1]$, Range $[0,\infty)$ $g(f(x))=\sqrt {1-\sqrt x}$, Domain $[0,1]$, Range $[0,1]$
The composite functions are computed by taking the inside function and placing it into the "x" value of the outside function: $f\circ g=f(g(x))$ The domain of any function consists of the values it can take on the x-axis, whereas the range consists of the value it can take on the y-axis. These values can be confirmed by graphing the function.