Solution
= Solution
Take the <function>
$$
\boxed{f:\mathbb R\longrightarrow\mathbb R,\qquad f(x)=-x.}
$$
Then $f(f(x))=-(-x)=x$ for every <real number> $x$, while $f(1)=-1\ne1$. Thus it is an <involution> different from the <identity function>.
= Solution
Take the <function>
$$
\boxed{f:\mathbb R\longrightarrow\mathbb R,\qquad f(x)=-x.}
$$
Then $f(f(x))=-(-x)=x$ for every <real number> $x$, while $f(1)=-1\ne1$. Thus it is an <involution> different from the <identity function>.