Answer:
[tex]f[2-f^{-1}(x)]=x[/tex]
Step-by-step explanation:
Given function is,
f(x) = [tex]\frac{x-1}{2}[/tex]
Equation form of the function will be,
y = [tex]\frac{x-1}{2}[/tex]
Interchange x and y,
[tex]x=\frac{y-1}{2}[/tex]
Solve for y,
y = 2x + 1
Therefore, inverse of the function 'f' will be,
[tex]f^{-1}(x)=2x+1[/tex]
Now [tex][2-f^{-1}(x)][/tex] = 2 - [2x + 1]
= -2x + 1
Value of [tex]f[2-f^{-1}(x)][/tex] = f(2x + 1)
From the given function,
f(2x + 1) = [tex]\frac{(2x+1)-1}{2}[/tex]
= x
Therefore, value of [tex]f[2-f^{-1}(x)]=x[/tex]
