Given:
The functions are:
[tex]f(x)=\dfrac{1}{2}x[/tex]
[tex]f^{-1}(x)=2x[/tex]
To find:
The values of [tex]f(2),f^{-1}(1),f^{-1}(f(2))[/tex].
Solution:
We have,
[tex]f(x)=\dfrac{1}{2}x[/tex] ...(i)
[tex]f^{-1}(x)=2x[/tex] ...(ii)
Putting [tex]x=2[/tex] in (i), we get
[tex]f(2)=\dfrac{1}{2}(2)[/tex]
[tex]f(2)=1[/tex]
Therefore, the value of [tex]f(2)[/tex] is 1.
Putting [tex]x=1[/tex] in (ii), we get
[tex]f^{-1}(1)=2(1)[/tex]
[tex]f^{-1}(1)=2[/tex]
Therefore, the value of [tex]f^{-1}(1)[/tex] is 2.
Now,
[tex]f^{-1}(f(2))=f^{-1}(1)[/tex] [tex][\because f(2)=1][/tex]
[tex]f^{-1}(f(2))=2[/tex] [tex][\because f^{-1}(1)=2][/tex]
Therefore, the value of [tex]f^{-1}(f(2))[/tex] is 2.
