ANSWER
[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]
EXPLANATION
The given functions are;
[tex]f(x) = \frac{1}{2} x[/tex]
[tex] {f}^{ - 1} (x) = 2x[/tex]
[tex]f( {f}^{ - 1} (x)) = f(2x)[/tex]
[tex]f( {f}^{ - 1} (x)) = \frac{1}{2} \times 2x = x[/tex]
Also,
[tex] {f}^{ - 1}( f(x)) = {f}^{ - 1} ( \frac{1}{2} x)[/tex]
[tex]{f}^{ - 1}( f(x)) = 2 \times \frac{1}{2} x = x[/tex]
In general,
[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]
