Answer:
Part 1) [tex]f(2)=1[/tex]
Part 2) [tex]f^{-1}(1)=2[/tex]
part 3) [tex]f^{-1}(f(2))=2[/tex]
Step-by-step explanation:
we have that
[tex]f(x)=\frac{1}{2}x[/tex]
[tex]f^{-1}(x)=2x[/tex]
Part 1) Find f(2)
For x=2
substitute the value of x in f(x)
[tex]f(2)=\frac{1}{2}(2)[/tex]
[tex]f(2)=1[/tex]
Part 2) find [tex]f^{-1}(1)[/tex]
For x=1
Substitute the value of x in [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(1)=2(1)[/tex]
[tex]f^{-1}(1)=2[/tex]
Part 3) Find [tex]f^{-1}(f(2))[/tex]
we know that
[tex]f(2)=1[/tex] -----> see part 1)
so
[tex]f^{-1}(f(2))=f^{-1}(1)[/tex]
we have that
[tex]f^{-1}(1)=2[/tex] -----> see part 2)
therefore
[tex]f^{-1}(f(2))=2[/tex]
