Answer :
Answer:
see the procedure
Step-by-step explanation:
we have
[tex]f(x)=\frac{1}{2}x[/tex]
[tex]f^{-1}(x)=2x[/tex]
step 1
Find [tex]f^{-1}(f(x))[/tex]
substitute the variable x for the function f(x)
[tex]f^{-1}(f(x))=2(\frac{1}{2}x)[/tex]
simplify
[tex]f^{-1}(f(x))=x[/tex]
step 2
Find [tex]f(f^{-1}(x))[/tex]
substitute the variable x for the function f^-1(x)
[tex]f(f^{-1}(x))=\frac{1}{2}(2x)[/tex]
simplify
[tex]f(f^{-1}(x))=x[/tex]
step 3
Compare
[tex]f^{-1}(f(x))=x[/tex]
[tex]f(f^{-1}(x))=x[/tex]
therefore
[tex]f^{-1}(f(x))=f(f^{-1}(x))[/tex] ---> is verified