Question

If f(x)=x-1/x+1 than proved that f(2x)=3f(x)+1/f(x)+3

Answer 1

F(x)=(x-1)/(x+1)
f(2x)=(2x-1)/(2x+1)

Then go to the claim that f(2x)=(3f(x)+1)/(f(x)+3) and plug in f(x) = (x-1)/(x+1) and simplify

f(2x)=(3f(x)+1)/(f(x)+3)

f(2x)=(3*(x-1)/(x+1)+1)/((x-1)/(x+1)+3)

f(2x)=(3*(x-1)+1(x+1))/(x-1+3(x+1)) ...
multiply every term by the inner LCD x+1


f(2x)=(3x-3+x+1)/(x-1+3x+3)


f(2x)=(4x-2)/(4x+2)
f(2x)=(2(2x-1))/(2(2x+1))


f(2x)=(2x-1)/(2x+1)
So this proves that f(2x)=(3f(x)+1)/(f(x)+3) is true when f(x)=(x-1)/(x+1)