examday

/TMUA

A function $f$ defined for all real $x$ is called self-inverse if and only if

Which of the following statements is/are true?

• I For every constant $c$, the function $f(x)=c-x$ is self-inverse.
• II If $f$ and $g$ are self-inverse, then the function $h(x)=f(g(x))$ is self-inverse.
• III Every self-inverse function is of the form $f(x)=c-x$ for some constant $c$.