SEAMO 2027 - Paper F - SET 07 - Self-study Question 19

Functions are defined by $f(x)=1/(2x+1)$, with $x$ different from $-1/2$, and $g(x)=x+1$. Find $x$ for which $ff=gf$, where juxtaposition denotes composition: $f(f(x))=g(f(x))$.

Composition convention: ff means f composed with f, and gf means g composed with f. Use only inputs for which both sides are defined.