Question

If f(x)=x+1/x-1,then prove that f{f(x)}=x

Answer 1

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


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


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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)