If f(x)=x-1x+1 then find the value of f(2x).
Step 1: Solve for the value of x.
Given: f(x)=x-1x+1
f(x)=x-1x+1(x+1)f(x)=x-1
xf(x)+f(x)=x-1
1+f(x)=x-xf(x)
1+f(x)=x1-f(x)
x=1+f(x)1-f(x)
Step 2: Compute the required value.
Substituting 2x in place of x
f(2x)=2x-12x+1f(2x)=21+f(x)1-f(x)-121+f(x)1-f(x)+1f(2x)=2+2f(x)+f(x)-12+2f(x)-f(x)+1f(2x)=1+3f(x)3+f(x)
Hence, the value of f(2x) is 1+3f(x)3+f(x).